I have no idea how long they last
Here's my interesting experience with 'cheap' bolt action rifles.
I bought several just for kicks (no Savages, so I can't comment on that make). Two Rem from Big Five, and one Mossberg from WallyWorld (it was $297).
Cheap rifles are generally uncomfortable, sometimes not easy to live with. The fit and finish aren't great. Often the controls are not easy to use. The magazines don't fit well, and/or the rounds don't fit into the mag boxes easily. The bolts aren't very smooth. The stocks are cheap and feel 'funny', mostly due to the grip surface but also the stock dimensions are just a bit unusual. The triggers are never good. Seldom are there good aftermarket choices to replace anything you don't like. If it comes with a cheap scope combo, the scope picture is generally a bit substandard (a little cloudy outdoors, to my eye). They have annoying parallax. The center of the glass is generally in focus but outside the center it gets unfocused.
But boy they shoot extremely well!!! I got sub moa from both cheap Remingtons (770 and 710, the 770 was by far the best) and a Mossberg (that one came with no scope, I mounted a nice Elite 4200 on it).
So the bottom line about cheap rifles (according to me):
They probably shoot better than you do,
but they're harder to live with than a nicer rifle.
So is it right for you?
I bet most owners shoot less than 2 boxes in the life of their rifles.
Take to the range once to make sure the scope is sighted in.
Then again after 5 years.
Maybe a deer hunt once every few years.
Then give it away to a family member.
Who literally never shoots it.
So what's wrong with that? Those cheap rifles are PERFECT for those owners.
And remember, they can shoot extremely well.
At least I can shoot them extremely well.