Comment by lxgr
They can; this usually shows up with a remark of "separate tickets".
There are considerable caveats when doing that – it's generally not advisable for connecting flights (you're essentially on the hook for missed connections etc.), and even just for separate outbound and return tickets it can mean trouble (e.g. if the outbound flight is cancelled, there is no obligation for the separate ticket to be refunded to you).
Granted I only travel with hand luggage, I never had any issues with cancelled or delayed flighs when booking separate tickets. Even so they are relatvely cheap. It is even cheaper if you book your return flight ticket separately.