Landlord asking for payment via a blank check

You mentioned blank checks twice in your post.  I think you must be referring to bank checks and not blank checks.  If it is blank checks they are requesting, DON’T DO THAT!!  They could write out any amount they want.
I’m assuming you meant BANK CHECKS; Aka:  cashiers checks, counter checks, money orders.   If management is requesting that you pay by Bank Checks, that is perfectly legal.  Most lease agreement have a provision that states that all money paid must be done by certified funds.  Certified funds is just a fancy way of saying guaranteed funds.  A personal check can take 5 to 7 days to clear, placing your landlord at a higher risk.  Bank Checks will never bounce.
Normally, property managers will start enforcing the rule after one problem with a personal check.  (Even if you were just late once)
 

Getting a certified check can be a pain.  That’s how I pay my rent.  One thing I learned was that my credit union will issue checks for no cost.  Try going to your bank or credit union.  Not a huge deal.