Hello, and welcome to the Piano World Forums!
I'm no expert, but the Yamaha U1 is a very popular instrument, at any age. Pianos do wear out if played a lot, but they also last a long time and the higher quality ones with the better components inside last a very long time.
And, that seems like a great price for that piano, age or not.
I recently purchased a 1969 Kawai K48A upright, which is probably similar in quality to the Yamaha U1, and it plays great and sounds great. It belonged to a music teacher and I'm sure was played a lot, yet it is in good condition.
That just goes to show that most serious musicians/teachers take good care of their instruments.
The cost of an inspection is around $75-$100 and may be worth the investment, unless you decide to go with your gut instincts, and there nothing wrong with that either IMHO.
Good luck and keep us informed!!
Piano enthusiast and amateur musician: "Treat others the way you would like to be treated". Yamaha C7. YouTube Channel