As a curio and relic they have a place. Some would say the Mosin Nagant delivers better value for the money.
In terms of being a top tier battle rifle the M14/M1A has about the shortest career in service of many. There are specific reasons for it being popular, but it has little to do with being ergonomically or mechanically superior. Just cool old wood and steel, for the most part.
The gun is just an update of the Garand to include the magazine it should have gotten from the first, and chambered in a much larger cartridge than he intended. Which goes to it being nearly impossible to use as a military full auto rifle, and also why it was quickly superseded by the M16.
They are a part of our history and available, unlike many others, get your money's worth in the purchase and enjoy it in it's simplest form. They are a great example of the era when the veteran's were celebrating their passing and held contests to prove how good they were. That's when 3 Gun started - when .30s were being obsoleted world wide, and old guys couldn't understand why.
If anything, they gave us ample reasons to move on, and still serve as an example of what we don't need in combat today. That is what most Curios and Relics do best.