NES:Disabling CIC Chip
As the NES was developed from the Famicom, Nintendo of America got the dubious double award of being the first console corporation to release anti-competitive measures - unlicensed title "blocking" and region locking.
Third parties still came up with more or less ingenious ways of bypassing it, but this is not particularly helpful if playing imports is desired - and, unlike on the SNES and N64, there is (mostly) no advantage in keeping the security chip, so it may be advantageous to remove it - which is exactly what happened at design stage to the NES-101.
Disadvantages
The main disadvantage is in fact with some unlicensed NES games, chiefly those that generate electrical spikes to attempt to glitch the 10NES - some have been reported to overheat without their "load"; of course, this logic can also be taken out of service afterwards.
A couple of first party titles do actually require the CIC-generated "cart reset" signal but, those titles being the Nintendo World Championships series, it is unlikely to ever affect most gamers :P
Additionally, there's the matter that anti-CIC mods have traditionally been misleadingly promoted as a solution to NES reboot loops: while this result will be achieved, it is not a panacea for bad connections and allowing a game to run in such state may in fact promote save corruption, for those with directly mapped SRAM.
Classic method: 2 keys and no locks
The 10NES system works through two equal chips trading totally-not-random sequences, with (only) the console-side one generating a reset if not satisfied.
As the chips are the same, pin 4 is pulled either up or down to switch it between respectively console or gamecard duty, therefore it can be disconnected from the PCB and shorted to ground.
Complete removal and replacement
On the other hand, ignoring its protection aspect, the 10NES can be considered a fancy reset generator, which fires (to pin 9) on internal conditions (key mismatch) as well as external ones (reset button - pin 7).
to be written
Full bypass
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