I had a double lensectomy done in 2000 at age 56; it was not for cataract but for correction of the extreme myopia (short-sight) that I had had since birth.
A bonus, as the surgeon said at the time, was that I would not require future cataract treatment.
I was assured that the lenses (IODs) would never move on the eyeball; they are retained by tiny "claws" called haptics.
In about 2015 I noticed a change in the sight of one eye; the (different) specialist that I consulted could find no problem at first but I insisted and he finally found the IOD. It had slipped off the front of the eyeball and travelled around to the back.
The following days were dramatic; he arranged an urgent appointment with a surgeon, who operated in his clinic theatre the next day. On the following day, after checking the results, the surgeon, with another surgeon, operated again at the clinic but suddenly suspended matters and said "Meet you at the hospital this afternoon".
After a couple of hours in the hospital theatre digging-around in my eye, he and another surgeon managed to put the lens back in proper position.
This was all done, as is necessary in eye surgery, with only local anaesthetic; it's highly-traumatic to hear surgeons discussing the problem while digging-around in your eye with what feels like a crowbar.
Afterwards I felt as if I'd fought ten rounds with Cassius Clay; it was at least six months before my life and my eye returned to normal.
Simple replacement would, of course, not be as traumatic but I described my experience to provide data for your decision.
I would just add that I think your eye doctor gave you good advice.