I don't see why this is an issue at all. You can have tailored clothes delivered to your room, or a personal shopper. You can have meetings with people of your choosing come up to your room. In some places, from what I heard, you can even have "guests" come up to your room. Pizza is no big deal. I'm sure it happens all the time for bachelor parties in luxury hotels all the time too.

It's not like lobby dress codes are an issue or the pizza delivery person is using the pool.

You might find that for security reasons, you might have to come down to the lobby to get the food. Or maybe, for example, in a Near East hotel the delivery person might not be allowed past the parking lot, or maybe your pizza gets searched.

Order away I say. Don't let anything get in the way of your enjoyment of pizza.