I know that other role playing games have a Permanência spell that has a sole purpose of giving other spells a permanent duration, but 5e seems to have no such spell. Is this because it would be overpowered or is it something that I have not noticed?
It would not only be overpowered, but it would also break the game design philosophy of 5e.
5e is a system that avoids stacking effects. If you want a small selection of permanent spells you have the options of Desejo, creating magical items and granting epic boons.
While this question is not strictly a duplicate, it has been answered in the following threads: Como os feitiços se tornam permanentes no 5e? e Quão explorável / equilibrado é esse feitiço de homebrew: Permanência de Feitiço?
The most notable design-philosophy considerations in 5e are how concentration spells avoid stacking effects, how advantage rolls avoid stacking, and how 5e generally streamlines its design.
Further considerations are how this spell would affect the world in which the game takes places. GMs have divergent opinions on whether a world has to be alive containing economic-, taxonomic- and ecological systems that are internally consistent. Permanency of any kind has everlasting effects in a society in which it is available, even when it is restricted to affect a limited amount of spells.