Yes, it's rude. You don't know what their finances are like, how they manage bills, what their income is, when they get paid, what other checks they're waiting to clear, etc.
If you had had my check for three weeks and it bounced, I would be calling your supervisor or whomever is above you. I balance my checkbook very well and always make sure I have reasonable funds available. However, I, like many others plan for the funds to be available in the few days to a week after the check is paid to the right person. Extra bills, groceries, miscellaneous items, etc, all cause my account to drop after a few weeks until the next paycheck appears. What I do with my money and when is none of your business.
If you are not a responsible enough landlord to deposit a check right away, it's on you, not the renter. When we make a payment by check, we plan accordingly and generally anticipate said check to clear with in 7-10 days, not three weeks.
Use some common sense and courtesy next time will you?