Chains, cassettes, and chainrings are replaced to avoid sudden and catastrophic failure of the drivetrain. Sure, the chain might just slip a little, which might not be catastrophic, but catastrophic consequences are easily possible if something should suddenly and unexpectedly break.
For starters, imagine what might happen if the rider were pedaling at full force to get up a steep hill or accelerate quickly, and then the chain broke. Chains most often break when the rider is pedaling very hard. The sudden change in resistance of the pedals could easily throw the rider off the saddle or the pedals, or off the bike entirely. So the rider could quite easily be injured. If the rider flies off the bike while surrounded by cars in traffic, or while pedaling along a steep mountain trail, then the rider could be killed.
Then there is the possibility of damage to the bike. The drivetrain of the bike could easily suffer further damage. The rest of the bike could easily be damaged by the flailing chain, or by crashing into a solid object because the rider is no longer there or is falling off.
Whether or not to keep up with maintenance is your choice, but in my opinion not keeping the drive train in good condition to save a little money on chains, cassettes, and chainrings is false economy. Medical bills and lost wages are far more expensive than easily-replaceable bike parts. If you want to save money, learn to do the maintenance yourself rather than paying a shop to do the work. Or maybe a local bike co-op can help you fix it very inexpensively. If you can't afford to maintain the bike over the long term, then you're probably better off selling it than riding it.
My personal story: many years ago when I was a (nearly) starving student, I was riding a ten-speed BSO that someone else had abandoned. I lubricated the chain when it squeaked and trued the wheel enough to not be annoying, and that was all the maintenance I felt like doing, because I hadn't paid anything for the bike, and because I preferred to spend my limited funds elsewhere. The chain had been skipping a little. One day I jumped on the bike and pedaled as hard as I could, because I liked to spice up my day that way. (I still do that sometimes, nearly 30 years later.)
Unfortunately my chain was quite worn, which caused it to stretch. Chains don't actually stretch, but the little pins, rollers, and plates wear, which makes the parts be a little further apart on tension. The stretched chain meant that the force of the chain was not resisted equally by every tooth of the rear cog that the chain wrapped around. Instead most of the force was resisted by the last tooth. The last tooth broke off, and then the chain broke off a few more teeth, and then the chain itself finally broke.
I had been standing on the pedals like a sprinter, leaning forward. My foot shot down when the pedal suddenly stopped resisting me, and over the handlebars I flew. I landed in the gravel-strewn asphalt parking lot on my forearms. I had badly-bruised elbows and road rash all over both forearms. Picking gravel out of the road rash in the shower was quite painful. I couldn't afford a hospital visit, being in the US, so I made do with first-aid cream. My arms took two or three days to scab over completely, and during that time I could not rest my arms on a desk or table; instead I had to hold my bloody arms in the air, disgusting my fellow students. I think complete healing took about a month. The bike was a total loss.