Cheesecake doesn’t make you think of...
What one thinks doesn't matter. Because thinking has nothing to do with this technique.
...Shakyamuni said...pali canon...mahayana sutras...primal vows...
Scriptural relevance doesn't matter either.
What matters is what you are doing with your awareness. In this meditation technique you are directing your awareness at a thing (the repeated phrase) and holding it there. Like you would hold a thing in your hand.
It doesn't matter if the thing that you hold is a pebble, a grape or a chip of wood. It's the same holding.
This nembutsu meditation is a variety of samatha. The "object" in this case being a scripturally-relevant phrase.
The phrase is not chosen because the phrase has special power. The phrase is chosen because we like scripture.
"anchor like function" and community standards aside...
The central thing that the technique does. The stillness, clarity etc. For that it doesn't matter at all.