I'm a bank teller - let me clear this up.
First of all, to answer the OP - you can do that, just write out the check, get the account number, write "for deposit only, acct # xxx-xxxx-x-xx" and you're done.
The purpose of endorsements is for checking cashing. When you endorse a check, you make yourself liable for the funds. Endorsing the check gives the bank authorization to remove funds out of your account if the check is stopped during processing. Basically, if the bank can't collect from the check, they collect the funds from your account.
You cannot cash checks without an endorsement. Generally the teller is supposed to compare the signature on the ID vs. the signature on the endorsement, or ask you to endorse it in their presence.
Word to the wise, NEVER endorse your checks before you get to the bank. As soon as you endorse it, if it's stolen, it can be cashed, or deposited into another account.