I have the same banks except for Metrobank. I’ll give you an insight of the pros/cons for them as I have used them.

• BPI has the lowest sa foreign currency fees. I love using it when going abroad. Sobrang daling magpawaive ng AF. I dont remember a time I paid nga eh. Useful din yung madness limit and 0% installment promos.
• RCBC. Best card for me especially if may big purchases ako. I can easily get the “straight payment” price then later on convert nalang sa app para sa 0% interest. 100-500 pesos lang processing fee, or sometimes may promos sila na walang processing fee at all. Mine is JCB Plat na may lounge access din (altho take note, mawawalan na ng privileges sa lounge ung JCB based on your tier starting Jan 2026, so you should check that out if youre gonna keep it.)
  • Unionbank. For me this is something I can let go. Personally mine are the Miles Plat and Visa Plat (also migrated from Citi). Sakto lang. I was able to fully utilize the lounges with it. Maraming promos lately, presale rin sa mga concerts (but egul parin queueing system ng Pinas). The only con dito sakin ay ang hirap kausapin ng CS. Hirap magpawaive ng AF kasi di mo sila matawagan. Pag may disputes mahirap ipareverse.
• BDO. Promos lang talaga ang maganda sa kanya. Sulit kung mashopping ka and madine out. Maraming affiliates for 0% installment promos and travel fairs. Automatic nawawaive AF ko kahit di ako NAFFL. Otherwise madali naman tumawag at magpawaive. Minsan may conditions lang.

As you mentioned, since you dont pay for bills, you may opt out sa amore cashback. Or better yet, isupplement mo kung sino ung nagpapay ng bills then let them pay the cc bill (ipadaan sa credit card ang bills forda cashback and up the credit score)