I can only think of some issues you have to worry about.

You should/need still keep track of the cards. But more cards means more to track. If you are up to the task then it's not really a problem. A spreadsheet and credit card binder would be useful. But consider that you will want to (a) physically secure the card against unauthorized persons using it (b) monitor them for unauthorized use (setup notifications to warn you if someone uses them in fraud) (c) More accounts you will want to keep open. It can hurt your credit if accounts are closed and your average length of credit goes down. You may have to do this by buying something small like a candy bar with the card once a year. Usually your bank will send you a letter if they are going to close your accounts due to inactivity (d) make sure autopayments are on because if you do make a small purchase to keep the account open you don't want it to become past due and kill your credit. (e) it's more online accounts to secure. If you do it you may have accounts with many banks. You will have to secure those accounts against online attackers. You will want to have strong passwords for each and if they offer it 2 factor authentication. (f) More addresses/personal information to update if something happens like you move. You will want to keep your addresses current for all the cards. CC companies send out promotional or informational mail. You don't want that going to an old address where someone might intercept it and then commit identity theft or fraud because some mail from your credit card wasn't sent to your current address because you didn't update it. (g) more accounts that could be compromised in a data breach (e.g. https://www.nbcnews.com/business/consumer/us-bank-data-breach-impacts-some-credit-card-accounts-rcna54594)

If you can handle that sort of stuff there isn't a financial problem with what you are discussing. It's just logistically more you have to handle.