My consoles are old, relatively, tho I do have a Yoshi 3DSXL, which may be considered newer. (I'm in UK, does that make a difference?)
The screen blacking out - well mine does this at load times, sometimes a second or two longer than I would expect it to be - I have put it down to the amount I have on the game - 4 human characters, PWP plus cafe/police station & stuff on main street - a lot more data on the cart, hence possibly slightly longer load times. I do have the cart versions of the game.
I don't play other games but I do see a few second wait (with a black screen) when I am loading system settings/data mangement (the logo with the spanner).
I do not think my 3dsXL's are broken in any way, would have to be more than this before I thought there was a problem.
They all have a gap between the top screen and the hinge - does that make them older versions?
Getting a new console - I'm waiting to see what the reviews are like on the new 3dsXL
Edit: - my screen does not go black while I'm playing apart from at load times, ie when you get the little train or kappn's boat symbols in bottom right - sometimes the load time does seem a bit long.
I never pause the game, just play, press start to finish and then the home button when I see 'press A' come up on the screen. I try to be careful when saving.