is it possible to request personal checks with the account number partially hidden?
No. The whole point of the account number is so that the banks that process the check can identify the account, so they know what account to take the money from. If there is not a complete account number on your check, how could they do that? If there isn't enough information for a fraudster to identify your account, then there isn't enough information for a legitimate user to identify your account either.
Is this a security issue? Sure. But it's a relatively minor one. Normally no one will see your check except the person you gave it to and the banks that process it. The person you gave it to could copy the number and then print counterfeit checks or enter it into a computer and make fraudulent ACH charges. That's pretty much the same problem you have with credit cards: Someone you give it to to could copy the account number and then make fraudulent charges. This happens, of course, but it's relatively rare.
Okay, technically, they don't HAVE to print your account number on your checks. One could imagine a system where each check is assigned a unique number that can only be used once, and those numbers are not sequential or otherwise easily predictable so you can't figure out what the next number is from seeing any one number. Or I'm sure some clever person could come up with some better scheme to make knowing someone's account number useless. But it would be a pain, and the fact that no one has done it is probably evidence that the amount of fraud isn't worth the trouble. It's cheaper for the bank to just eat the loss now and then than to come up with some complex scheme to prevent it.