It really shouldn't be. I had a card compromised in the Target breach and they sent me a new one without my intervention. I've had fraudulent charges made before, and it's been trivial to get it fixed.
I've never had a checking account compromise, but I'm pretty sure it would be a massive pain in the ass by comparison.
The Target compromise wasn't a minor pain for everyone. A friend's bank reissued her credit card. Which caused a payment she had made to Time Warner fail. She was also in the middle of moving, which caused even more headache and a potential hit on her credit for late payment, because apparently Time Warner doesn't even attempt to notify you if your payment fails.
I'd put the blame entirely on Time Warner for that one. The Target breach is entirely incidental to the store. The same thing would have happened if the card had expired naturally, or been closed for other reasons.
Mentioned above, but relevant here too. I've had my debit card compromised several times, and it was still trivial - one phone call and was refunded in a few days.
Debit cards mostly give you the same protections as credit cards. They're worse in that the money comes out of your account immediately (but is supposed to be returned when you report fraud), and the rules are different and less favorable if your PIN is also compromised, but overall it's not too bad.
A compromise of your routing and account number for your checking account is potentially much worse. It's harder to take advantage of, but it's also much harder to fix.
(I'm not sure if you were treating the debit card as analogous to credit cards or account numbers, so treat this as confirmation/correction/elaboration/whatever as appropriate.)
Did the bank charge you for the replacement cards? Is there any real reason not to just regularly - say every 3 months - request a new card for peace of mind?
They did not. That stuff is basically a loss leader for them.
From what I recall with the Target incident, their cost is something like $2-5 for each replacement card, so it's not entirely trivial. If you requested a new one on a regular basis for no good reason, they might put a stop to it one way or another.
As far as peace of mind goes, since the consequences are so mild, I wouldn't worry about it.