Mendicants in the 21st century

Aren't Buddhist monks traditionally mendicants?

Yes I think that's clear from stories told in the suttas, as well as in the Vinaya.

what if any differences there are between his advice then, and the ideal now

I think that tradition is still followed by Theravada monks (and laity), with results including like this.

Or this: The Food of Kindness

My heart grew bright with compassion. I knew that I was standing there to let my bowl be filled again and again by those who love Truth. Hungry or not, I had every right to receive what they freely gave. I was not abusing that beauty because it was not for me that they filled the bowl.

A corollary is that these monastics can't abide where the lay community won't support them. I think that a lay community will sometimes invite a monk to come and establish themselves in a place.

Also, over the centuries some non-Theravada schools of Buddhism have, by necessity, abandoned alms-going as a means of support. I suppose that's how stories like No Work No Food come to be.

This answer might sound idyllic. Sometimes it's a difficult life, for example you might find Laughter Through the Tears: Kosho Uchiyama Roshi on Life as a Zen Beggar is worth reading.

Conversely there's also a monograph called The Broken Buddha which suggests that, sometimes, monks and monasteries are given what could be seen as an over-abundance.

Traditionally monks are allowed to receive the "four requisites", for example food, but not money. That remains true in some schools; but not true in others (hence a story like, Tetsugen and the Sutras).

A monastery might have lay people, who help administer money associated with a modern monastery (to pay for electricity for example).

I also recommend this paper (it's on-topic to your question): Growth and Development of Buddhist Organizations: An Organic Process of Cooperation. It's written by a Theravada monk, from Sri Lanka, who established a society and monastery in the United States. It details ways in which customs/expectation of lay society were (in around 1985) different in the States than in Malaysia or Sri Lanka, and some experience with asking or not asking for money.

You may wonder how the Theravada monks can do all these things, because we believe in strictly following the Vinaya. We did these things only to get the temple started, and the rules we broke were only the rules that do not hurt anybody, such as not handling money and not to drive a car. Actually, there was never any rule against driving a car, of course; the Buddha told the monks not to ride animals or be pulled in a cart by animals, out of compassion, because they are living beings. With the modern car, you are the only animal.

Some of the rules are just tools of etiquette. So among these minor rules, it may be acceptable. These must not be rules which concern our main principles of non-harm, non-greed, and non-hatred.

Aren't Buddhist monks traditionally mendicants?

Yes, it was so in the past. It is so in the Theravada Tradition in the present, and it will be so in the future as long as the true dhamma is alive. The scriptures itself describe that way of life as:

”A monk is content with his robes to protect his body and alms food to sustain his life; whenever he goes out he sets out taking only his requisites along with him. Just as a bird, wherever it goes, flies with its wings as its only burden; in the same way a bhikkhu is content with robes to protect his body and alms food to satisfy his belly.”

In the recent past when Ajahn Sumedho asked Ajahn Chah’s permission and blessings to establish a ‘Vihara’ in London, England, UK., he emphasized that the bhikkhus should go out into the streets on a daily alms-round – to keep the bhikkhus tuned in to the principle of alms-mendicancy. (What no one expected was that this would result in the sangha being offered a sizeable tract of woodland in West Success – as a result of a chance encounter with a jogger crossing Hampstead Heath in 1978).

Is there any difference in principle between then and now?

It is not so for the true disciples of the Supreme Buddha who walk this Noble Path. For them it is a form of giving for those fortunate few laypeople who will get this rare opportunity to give alms to the Sangha. The scriptures (The Dakkhinavibhanga Sutta) state that alms given to recluses who follow the Noble Eightfold Path yield great results just as seeds sown on fertile, well-prepared, well-watered fields produce abundant crops. The sutta gives a list of persons to whom alms can be offered and the merit accruing therefrom in ascending order.

A thing given to an animal brings a reward a hundredfold. A gift given to an ordinary person of poor moral habit yields a reward a thousandfold; a gift given to a virtuous person yields a reward a hundred thousandfold. When a gift is given to a person outside the dispensation of Buddhism who is without attachment to sense pleasures, the yield is a hundred thousandfold of crores.

When alms food is given to one on the path to stream-entry the yield is incalculable and immeasurable. So what can be said of a gift given to a stream-enterer, a once-returner, or a non-returner?

A bhikkhu is literally 'one who lives by alms'. However, it is not the same as a beggar because the laity that provide the alms get something in return - access to the wisdom and insight of the bhikkhu. Kasi Bharadvaja Sutta gives the Buddha's words to a confrontational Brahmin who refuses to give alms to the Buddha because he does not believe the Buddha 'works for it'.

The conditions for surviving on such alms depends on a laity that is interested in learning about the Dhamma (and hence supporting those that strive to gain direct knowledge of it). Really, the world is much more interconnected, there are far more people, and finding some who would be interested in your message would not be that tough imo! Finding a quiet and secluded spot would be more difficult imo! Here's a story I found: https://bhikkhucintita.wordpress.com/2014/01/28/alms-round-in-america/ I guess if the cultural knowledge is not there, it is a matter of educating your laity and getting them into the practice!