Why are Fallout's computers so backwards?
The world of Fallout has had a Divergence from our world somewhere after WW2. Where we went on big in computers and invented the transistor in 1947 (an essential component for making small computers), the world of Fallout didn't invent it until 2067, instead focusing on things like nuclear power, laser rifles and giant death robots.
Note: I did not write the Fallout universe lore. There are obviously some inconsistencies and/or plotholes in the universe, but I'm just reporting the information I found on the wiki. What appeared to have happened is that they never got into the miniaturization drive we pushed for with computing, but they kept increasing the performance of the components.
Out of universe, Fallout is a "retrofuturistic" setting: the setting is based on the future as imagined at some point in the past (in this case the 1950s). The computers are just a small part of that.
Other common uses of this device include steampunk, so this 1950s future is sometimes referred to as "atompunk".
Possible speculation: higher-yield powerplants in vehicles and in the power grid from extreme nuclear utilization reduced the impetus for miniaturization that led to the computer age. If you look at very old electronics, vacuum tubes and all, and look at new electronics, you notice something very interesting. In general, older electronics use a lot more input power for the same output, and they are usually considerably heavier.
Weight is an issue mainly when you transport things - in gasoline powered cars, extra weight reduces fuel economy. If you're driving a nuclear-powered car however, the economy loss for heavy equipment is probably minimal.
As said, older systems tended to use more power. Again, not a problem if you're putting nuclear reactors everywhere. You can see this especially in older televisions and radios. No incentive to economize.
Lastly, one possibility is electromagnetic interference. See, when a small reactor goes boom, just like when any nuclear bomb goes off, there's significant EMP output, that can damage electrical equipment for miles around. Some older, tube-type (or "analog") equipment was more resistant to EMP spikes than modern, solid-state equipment. Since nuclear power was apparently in every household, maybe that was a concern? I know high-altitude EMP tests (Operation Fishbowl, of which Starfish Prime was the largest) concluded that a high altitude explosion of relatively small bombs could EMP thousands of miles of surface area.
Just some thoughts. The possibility we're overthinking it a bit exists. But I think some of these idea hold a teensy bit of water