There are two things that limit the life of a Gen 1 'scope:
First, the light amplification is accomplished with a vacuum tube. Eventually, vacuum tubes burn out. But that's operating life, not shelf life.
Second, the vacuum tube requires a very high voltage. These 'scopes typically run off of a rather low voltage battery. Getting from the low- to the high-voltage is done with a switch-mode power supply. Back when these 'scopes were made, mid-80's typically, the capacitors used in switch-mode supplies were liquid-dielectric electrolytic type. The liquid dielectric evaporates over time giving a shelf life of perhaps 20 years.
Bottom line: most of the Gen 1 ' scopes are on their last legs.
Of course, those caps can be replaced easily.
Of course, someone will now chime in saying how their 20+ year old Gen 1 is still going strong. I'm sure it is. I've got one myself that still seems to work fine. And any given unit may go for a lot longer. But, overall, they are approaching the statistical average end-of-life for those capacitors.