An unamendable constitution protects democracy from bad political actors.
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Imagine a scenario where a politician with dictatorial aspirations is voted into office by the majority of the popular vote. Once in office, the leader acts on their dictatorial urges, dismantling the democratic system and the institutions designed to protect it.
Without an unamendable constitution, this leader could theoretically turn a fully functioning democracy into a dictatorship overnight. Unamendability functions as a safeguard against the destruction of democracy. Democracy is its own greatest threat. The unfettered freedom of the electorate to delegate power to any individual or political party means that inevitably, on an infinite timeline, it will eventually bestow power on someone/a party that seeks to undo it.  Unamendable provisions in a constitution protect democracy from its own self-destruction and prevent the threat of an authoritarian or totalitarian takeover.
Unamendability doesn’t only protect democracy, it also protects outdated principles. The American Constitution protected slavery. In other parts of the globe, unamendable constitutions have protected the oppression of minorities. These unamendable constitutional elements foster division and lead to division in society and human rights abuses. Under a fully democratic political system, the electorate needs to have the ability to remove these abhorrent elements from their constitution. If that means their democratic principles are left slightly more exposed, then so be it; for it is only by making every element of the constitution amendable that democracy can be fully guaranteed. The claim that unamendability protects democracy better than an amendable constitution is also highly dubious. If the majority of the electorate demands constitutional change but the political and legal system offers no avenue for it, the population is far more likely to take up arms and pursue constitutional change through violent means. Therefore, rather than protecting democracy, constitutional unamendability hastens its downfall in highly engaged, politicized societies.
[P1] A democracy will eventually give someone with dictatorial ambitions power. [P2] When this happens, without an unamendable constitution, they will be able to dismantle the country's democratic institutions. [P3] An unamendable constitution prevents a dictator removing democracy. [P4] Therefore, an unamendable constitution protects democracy better than an amendable one.
Rejecting the premises
[Rejecting P4] An unamendable constitution offers no outlet for constitutional change. This increases the likelihood of civil unrest and violence. Therefore, an unamendable constitution does not protect democratic processes better than an amendable one.