The recipient is the one who decides the unlocking requirements, not the sender.

When you send Bitcoin to someone, they provide an address. That address is a hash of a script they’ve chosen. You don’t get to choose the script parameters.

What the sender could do is make a UTXO that, say, promises you some coin, and also promises coin to a bunch of other folks. To use your coin, you first need a transaction that pays out to you (and everyone) and then a second transaction to actually spend. So, the fees could be potentially high, since it takes two TXs and there may be e a lot of outputs (many bytes) for the first one.