Why isn't Buddhānussati more popular in the West?

The Kitagiri Sutta says:

"And what is the individual who is a conviction-follower? There is the case where a certain individual does not remain touching with his body those peaceful liberations that transcend form, that are formless, nor — having seen with discernment — are his fermentations ended. But he has a [sufficient] measure of conviction in & love for the Tathagata. And he has these qualities: the faculty of conviction, the faculty of persistence, the faculty of mindfulness, the faculty of concentration, & the faculty of discernment. This is called an individual who is a conviction-follower.

I think the conviction follower and faith follower refers to the same thing.

The faith follower also has faith and conviction in the impermanence of various phenomena, according to SN25:

"One who has conviction & belief that these phenomena are this way is called a faith-follower: one who has entered the orderliness of rightness, entered the plane of people of integrity, transcended the plane of the run-of-the-mill. He is incapable of doing any deed by which he might be reborn in hell, in the animal womb, or in the realm of hungry shades. He is incapable of passing away until he has realized the fruit of stream-entry.

Faith in the Buddha and the teachings would lead one towards stream entry. But it's insufficient by itself.

According to the Vera Sutta (AN10.92), to achieve stream-entry, one needs to still the five forms of fear and animosity, attain the four factors of stream entry and rightly see & rightly ferret out through discernment, the noble method.

The five forms of fear and animosity are caused by:

• Taking a life
• Stealing
• Illicit sex
• Telling untruth
• Heedlessness through intoxicating substances

The five precepts are training rules undertaken to abstain from the above five.

The four factors of stream entry are:

• Verified confidence in the Buddha
• Verified confidence in the Dhamma
• Verified confidence in the Sangha (the 8 types of individuals)
• Has virtues appealing to the noble ones: untorn, unbroken, unspotted, unsplattered, liberating, praised by the wise, untarnished, leading to concentration.

To elaborate on the fourth factor of stream entry, we find some details in the Thana Sutta:

And then there is the case where one individual, through living with another, knows this: 'For a long time this person has been untorn, unbroken, unspotted, unsplattered in his actions. He has been consistent in his actions. He has practiced consistently with regard to the precepts. He is a virtuous, principled person, not an unprincipled one.'

The fourth factor of stream entry is basically to be virtuous and principled, which includes keeping the five precepts. Virtue (sila) is defined by Right Speech, Right Action and Right Livelihood.

In the Nandiya Sutta, there is further elaboration:

"Furthermore, the disciple of the noble ones is endowed with verified confidence in the Dhamma... verified confidence in the Sangha... virtues that are appealing to the noble ones: untorn, unbroken, unspotted, unsplattered, liberating, praised by the wise, untarnished, leading to concentration. Not content with those virtues pleasing to the noble ones, he exerts himself further in solitude by day or seclusion by night. For him, living thus heedfully, joy arises. In one who has joy, rapture arises. In one who has rapture, the body becomes serene. When the body is serene, one feels pleasure. Feeling pleasure, the mind becomes centered. When the mind is centered, phenomena become manifest. When phenomena are manifest, he is reckoned as one who dwells heedfully.

This then leads to the "noble method".

The noble method mentioned here is understanding dependent origination and its relationship to the ending of suffering.

Interestingly, in the Gihi Sutta, the householder only needs to keep the five precepts and fulfill the four factors for stream entry (known in this sutta as the four pleasant mental abidings) in order to attain stream entry. The last "noble method" is not mentioned.

Also this study guide on stream entry and this commentary might be interesting to you.