Using postfix aliases as a simple mailing list without sending mail to sender

Solution 1:

No, such a setting does not exist.

But as commented, it could be done if one were so inclined. But it will be quite a hack, with negative consequences for the future. You'll accumulate technical debt.

When it comes to simple solutions, at literally all places I worked at, the mailing lists (to be more exact; this is a distribution list) were implemented exactly the way you did; so that a sender received a copy of his own mail.

This is not bad, quite the contrary, as with modern MUA's this enables them to display a threaded view in case of a discussion (granted, this shouldn't be too frequent on distribution lists, but happens still and is of some use). And frankly, people are used to it. Some even go as far as automatically CC each mail they send (it might sound crazy to others, but some people function differently and use their inbox for all kinds of stuff..ask the GMail guys).

If someone does not like this behaviour, he or she should set up an according filter rule on his own MUA.

This is the simplest way I would implement it. For other cases, I use mailman (which is very easy to setup) or the facilities provided by the mail server software.