From what you hear it's that they have bills to pay. If a publisher doesn't know your name, they're not going to assume it's an automatic best-seller so they're less likely to actually look at your work to see if it's worth it.

Also, to pay your bills before the publisher actually prints the book, you have to find one way ahead of you finishing the book, meaning that you have to send them an unfinished manuscript, further hurting your chances - but if they like it you get that money before it's done, with the caveat that they're gonna sue if you don't deliver.

Authors have to submit manuscripts to publishers individually (or, in some markets, agents who work with multiple publishers in the same niche).

Publishers get showered with manuscripts. Very small percentage of them are what publishers deem will meet market goals.

In standard publishing contracts, the author gets paid an advance. This is basically the royalty percentage for the entire first print run. It's not refundable. It represents the trust the publisher puts on the author, and if the publisher can't sell all copies, well, tough for them. (They'd probably just not work with that author again.)

Getting to that point is a pretty massive hurdle to clear for first time authors.

So no, authors don't really get to pick their publishers. The only scenario where people get to pick their publishers is some celebrity deal bullshit.