No. Power cycling is normal operation. Cartridges use mask ROM (read-only) or flash memory (save) — neither wears from power transitions.
Why It's Safe
No write on boot: Console reads header → loads ARM9/ARM7 binaries → executes. Save data only written when game explicitly saves (menu, auto-save, sleep).
Contacts designed for cycles: Edge connector rated for 10,000+ insertions. Power on/off doesn't stress contacts.
Capacitors buffer: Console's power regulation smooths inrush; cartridge sees stable 3.3V.
Actual Risks to Cartridges
Physical abuse: Bending, dropping, liquid, dust in contacts.
Save corruption: Power loss during write (saving) — not during idle/play. Always wait for "Saving..." to finish.
Battery (GBA/DS carts with RTC): CR1616/CR2025 coin cell dies ~10–15 yrs → time events stop, save still works (flash). Replaceable.
Counterfeit carts: Cheap flash chips fail early — buy authentic.
Best Practice
Save → wait 2 sec → power off.
Store in case, cool/dry.
Clean contacts with 99% IPA + cotton swab if dirty.