What would happen if I don’t replace worn drivetrain components? What would happen if I took a entirely new drivetrain and just never replaced anything? Of course, I’d keep it clean and lubricated.
With 11 and 12 speed chains being as expensive as they are, the old adage of “replace the chain to protect the cassette and chainrings” starts to make less and less sense. If I skip two new chains, I save the cost of a cassette. Another skipped chain would cover new chainrings.
In other words, skipping three replacement chains would save me enough money to just buy an entirely new drivetrain. That is better than the normal approach, which -for the same money- would give me four worn out chains, a worn out cassette, and worn out chainrings.
Importantly, this avoids the issue of having a new chain on a worn cassette or some other combination thereof.
What are the downsides to my logic? I can think of a few right now:

decreased shift performance
increased risk of chain breakage (by how much?)
In my experience - breakage is not directly correlated to wear.  I've had bikes with unknown mileage on them, and have chosen to ride the transmission into the ground.
Generally the performance slowly deteriorates, with chain slip under power being a sign that things are getting bad.
Unlike other answerers, I've never had a worn transmission break and strand me or injure me.  The only time I snapped a chain is because I didn't reconnect it properly, and that one was perhaps half-worn.  I have twice wiped a derailleur with the rear wheel's spokes, but again that was misadjustment, not wear.
If you can afford to, replacing parts often helps maintain things in top-top shape, but for those of us with real world demands on our wallets, you can go quite far into the worn stage before it gets too much.  After all - you own it.
I find that climbs and going up grades are the most taking on the transmission and drivetrain so if its going to slip, its then, or when doing high power efforts like taking off from the lights.