And no, the numbers are very clear, presidential and semi presidential republics absolutely dominate the share of countries turning authoritarian.
Presidents do not need a majority trust of their parliament, support of their coalition nor party, as prime ministers need every single day. A PM is one vote away from having to resign, which is why those governments change much more often.
Presidents can claim popular mandate, prime ministers less so, you vote the party, which forms coalitions, not the candidate directly (albeit some parties change name to include the candidate name). This is incredibly important because it authorizes individual to do almost as they please and default to the fact that they were voted to do so.
Presidential and semi presidential republics naturally breed a personal cult that is difficult to replicate.
Mature developed countries have more to lose allowing individuals major adjustments testing their power boundaries nonstop (see this presidency in US) than to gain.