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).
You need to be more clear about what you meant by saying "never had issues".
The point is there might be issues because the second flight has no obligation to refund you if you're late (but they might still do out of generosity).
It's not like it's gonna happen all the time. So having data points saying that didn't happen is kinda pointless.
> Granted I only travel with hand luggage
That makes an enormous difference, since you usually can do your check-in online a day or more before departure.
I just had a flight where I had purchased my connections on separate tickets. When I arrived at the baggage drop-off, it was closed and no staff from the airline was anywhere. So I had to bring my big suitcase along through security and then the airline staff at the gate was friendly enough to check it in for me for free.
But if you're bringing anything in your checked luggage that security doesn't like, you will have to just leave that item at the airport. You might also have to pay a high fee to bring it to the gate instead of checking it, depending on airline. I had purchased my ticket directly from the airline, so maybe they treated me better because of it?
"separate tickets" are for 2 1-way tickets instead of a round-trip, not splitting a 1-way across a connection.