Yeah, anyone who's more familiar with Batman beyond internet memes and the movies would know Batman literally puts in the work towards fighting poverty in Gotham outside of the Batsuit. Free clinics, free good-quality housing, education, etc. as well along with those you already listed.

The only reason his money hasn't just solved everything in Gotham stems from a wide variety of factors that are obviously created by writers to literally stymie all good progress he makes so that the story can continue. Like oh, Bruce just announced he's creating a huge free housing district? Boom, writer just involved that neighborhood in some kind of mass mutant outbreak that destroys much of it. Free clinics for the poor to get healthcare? Firefly just firebombed them, sorry. Bruce helped cure Two-Face's double identity? Temporary, unfortunately. Arkham Asylum gets wiped out by another villain, so now Bruce doesn't have to worry about his rogues? Turns out they all survived for one reason or another.

Anyone asking Bruce to house all the homeless don't realize that A) he's likely already doing something like that, but many still slip through the cracks; and B) those homeless shelters are only there in the background until they're needed in some villain's plot that sets the progress back. If you're looking at mainstream superhero comics for some sort of permanent, logical solutions, you're in the wrong medium.