Look at the U.S. presidency since the 22nd Amendment. After FDR's four terms, we locked in a two-term limit, and since then no president has tried to hold power indefinitely. That's not a coincidence. It created a predictable off-ramp that forces parties to groom new candidates instead of clinging to an incumbent.
On the Philippines, sure, dynasties rotate family members. But that's a cultural problem, not a term limit problem. Without term limits, that same family would just keep the same person in power forever. At least rotation creates regular openings, even if imperfect ones.
You say lawmakers peak after a few years. I agree. That's exactly why two terms works. At year ten, the corruption risk and the incentive to preserve power start outweighing the policy expertise. Elections aren't the perfect check you claim—incumbents have huge advantages in funding, name recognition, and redistricting. Term limits level that field where elections can't.
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