What's the benefit of running own server in this case? Wildcard aliases is actually a standard fastmail feature, I use it a lot. No per-email setup needed whatsoever, I just give out <whatever>@mydomain.com, they all will reach my inbox. Haven't seen people sending spam to random aliases at my domain yet.
Yes, you can explicitly set up additional aliases that will bounce incoming mail (or redirect it). It's an option in "New Alias" screen - "Reject (bounce) all mail sent to this address (disable the alias)". While everything else not explicitly configured would get caught by the wildcard alias and delivered to the inbox you specified for it.