I worked in financial industry CSR for eight years. U.S. banking philanthropy is strategic in supporting business outcomes & tends to be driven by two things:
- CRA Act requirements
- geographic markets where they have business reach or potential https://twitter.com/MarketWatch/status/1354611584593756160

The Community Reinvestment Act was enacted in the 70s to counter racist redlining policies. It mandates that banks invest $$ & expand access to banking tools in low-to moderate- income communities. State Federal Reserves oversee & rank their compliance:
https://www.federalreserve.gov/consumerscommunities/cra_about.htm

You can search institutional CRA ratings here. Low/unsatisfactory ratings prevent banks from opening branches or expand to new markets so staying in good standing is incentivized. Philanthropic giving often complements local investments in these areas:
https://www.ffiec.gov/craratings/ 

Geographic market presence is the second driver. Banks often "pre-invest" in markets they want to expand into with grantmaking & community support. It helps them look good. Essentially they are buying goodwill. And banks love to compete on whose a better "community neighbor."

This isn't to say all bank philanthropy is driven by profit potential but most is. The CSRs I worked for had incredibly thoughtful people who used these tools to fund creative & truly catalytic work - but often took years to educate & convince higher ups to take the risk.

Some banks also inform their grantmaking based on employee interests (through Matching Gifts programs & other mediums). I don't know of any where this model substantially influences the totality of a grantmaking budget but worth mentioning.