Did the Buddha intend for everyone to be enlightened?

The Buddha does not have the intention for everyone to be enlightened.

However, the Buddha has compassion, which is his expression of alleviating the suffering of others. He is willing to teach everyone who is willing to listen to him.

So, the end goal of enlightening everyone is not his goal. However, his goal is to teach others who are willing to listen, and hope that they will also help others.

The teaching of others is his goal, and not the end goal of enlightening them. That's up to the people whom he teaches. It's in their hands, not his.

The Desanaa Sutta shows the 3 types of people he is willing to teach, to various degrees:

"Does not the Blessed One dwell in compassion for all living beings?"

"Indeed, headman, the Tathaagata does dwell in compassion for all living beings."

"Well then, Lord, does not the Blessed One teach Dhamma in full to some, but not so fully to others?"

"I will reply to this question, headman, with another. Answer as seems proper to you. What do you think? Suppose a peasant farmer has three fields, one excellent, one middling, and one poor, sandy, salty, with bad soil. Tell me: when the farmer wants to sow his seed, which field would he sow first: the excellent one, the middling one or the poor one that is sandy, salty and with bad soil?"

"Lord, the farmer who wanted to sow his seed would sow the excellent field first. Having done that, he would sow the middling field next, and the one that was poor, sandy, salty, with bad soil he might or might not sow. Why? Well it might do for cattle-food."

"Well, headman, that excellent field is like my monks and nuns. To them I teach the Dhamma which is lovely in its beginning, lovely in its middle and lovely in its ending, in spirit and in letter, I display to them the holy life, perfectly fulfilled and purified. Why? Because these people adhere to me as their island, their shelter, their resort, their refuge.

"The middling field is like my male and female lay-followers. To these too I teach the Dhamma which is lovely in its beginning, lovely in its middle and lovely in its ending, in spirit and in letter, I display to them the holy life, perfectly fulfilled and purified. Why? Because these people adhere to me as their island, their shelter, their resort, their refuge.

"The poor field that is sandy, salty and with bad soil is like my wandering recluses and Brahmans of other sects. To them I also teach the Dhamma which is lovely in its beginning, lovely in its middle and lovely in its ending, in spirit and in letter, I display to them the holy life, perfectly fulfilled and purified. Why? Because if they only understand a single phrase, it would long be for their profit."

The Kesi Sutta shows that, as an excellent teacher, he has various techniques to teach others, but he may give up on stubborn students:

"Kesi, I train a tamable person [sometimes] with gentleness, [sometimes] with harshness, [sometimes] with both gentleness & harshness.

"In using gentleness, [I teach:] 'Such is good bodily conduct. Such is the result of good bodily conduct. Such is good verbal conduct. Such is the result of good verbal conduct. Such is good mental conduct. Such is the result of good mental conduct. Such are the devas. Such are human beings.'

"In using harshness, [I teach:] 'Such is bodily misconduct. Such is the result of bodily misconduct. Such is verbal misconduct. Such is the result of verbal misconduct. Such is mental misconduct. Such is the result of mental misconduct. Such is hell. Such is the animal womb. Such the realm of the hungry shades.'

"In using gentleness & harshness, [I teach:] 'Such is good bodily conduct. Such is the result of good bodily conduct. Such is bodily misconduct. Such is the result of bodily misconduct. Such is good verbal conduct. Such is the result of good verbal conduct. Such is verbal misconduct. Such is the result of verbal misconduct. Such is good mental conduct. Such is the result of good mental conduct. Such is mental misconduct. Such is the result of mental misconduct. Such are the devas. Such are human beings. Such is hell. Such is the animal womb. Such the realm of the hungry shades.'"

"And if a tamable person doesn't submit either to a mild training or to a harsh training or to a mild & harsh training, what do you do?"

"If a tamable person doesn't submit either to a mild training or to a harsh training or to a mild & harsh training, then I kill him, Kesi."

"But it's not proper for our Blessed One to take life! And yet the Blessed One just said, 'I kill him, Kesi.'"

"It is true, Kesi, that it's not proper for a Tathagata to take life. But if a tamable person doesn't submit either to a mild training or to a harsh training or to a mild & harsh training, then the Tathagata doesn't regard him as being worth speaking to or admonishing. His knowledgeable fellows in the holy life don't regard him as being worth speaking to or admonishing. This is what it means to be totally destroyed in the Doctrine & Discipline, when the Tathagata doesn't regard one as being worth speaking to or admonishing, and one's knowledgeable fellows in the holy life don't regard one as being worth speaking to or admonishing."

The Maghadeva Sutta shows that the Buddha does not want his disciples to stop practising his teachings, and wants them to continue practising and teaching throughout the generations:

But now I have founded a good practice that does lead to disillusionment, fading away, cessation, peace, insight, awakening, and extinguishment. And what is that good practice? It is simply this noble eightfold path, that is: right view, right thought, right speech, right action, right livelihood, right effort, right mindfulness, and right immersion. This is the good practice I have now founded that leads to disillusionment, fading away, cessation, peace, insight, awakening, and extinguishment. Ānanda, I say to you: ‘You all should keep up this good practice that I have founded. Do not be my final men.’ Whatever generation is current when such good practice is broken, he is their final man. Ānanda, I say to you: ‘You all should keep up this good practice that I have founded. Do not be my final men.’”

Finally, it's up to people whether they want to become enlightened or not, according to the Mahaparinibbana Sutta:

"Therefore, Ananda, be islands unto yourselves, refuges unto yourselves, seeking no external refuge; with the Dhamma as your island, the Dhamma as your refuge, seeking no other refuge.

"And how, Ananda, is a bhikkhu an island unto himself, a refuge unto himself, seeking no external refuge; with the Dhamma as his island, the Dhamma as his refuge, seeking no other refuge?

"When he dwells contemplating the body in the body, earnestly, clearly comprehending, and mindfully, after having overcome desire and sorrow in regard to the world; when he dwells contemplating feelings in feelings, the mind in the mind, and mental objects in mental objects, earnestly, clearly comprehending, and mindfully, after having overcome desire and sorrow in regard to the world, then, truly, he is an island unto himself, a refuge unto himself, seeking no external refuge; having the Dhamma as his island, the Dhamma as his refuge, seeking no other refuge.

"Those bhikkhus of mine, Ananda, who now or after I am gone, abide as an island unto themselves, as a refuge unto themselves, seeking no other refuge; having the Dhamma as their island and refuge, seeking no other refuge: it is they who will become the highest, if they have the desire to learn."