1) The oil is likely PCB laden, if it leaks unexpectedly it's a major HazMat situation, high clean-up costs, long down time etc. Actually you will have some of those costs just to remove them, but it can be done during a scheduled shutdown, as opposed to more costly emergency situation where the added delay in getting anyone to come and deal with it can be very very expensive.
2) The oil must be periodically checked for dissolved gasses etc. as the equipment ages. Not doing so runs a risk of having it cease to function as an insulator. In m y experience people who are too cheap to change out old obsolete equipment are likely too cheap to do proper maintenance as well.
3) If it does fail, nobody has made an oil immersed motor starter in the US in 50 years that I am aware of, so there will be no parts, no like-for-like replacements. Again, swapping it out with a regular NEMA 7 motor starter in an emergency shutdown situation will cost WAY more than doing it now preemptively and being able to shop for, and wait for, a NEMA 7 starter.
All that said, in both situations where I have come across them, neither (cheap) person decided to do the right thing, electing to "take their chances"... One of those resulted in a fire just 6 months after I left.
Good luck...