I tried what you said in the most realistic simulator we have, Kerbal Space Program, assuming like you that a gentler approach would be better. And I learned that no, that most certainly is not better.

What you need to protect is on the inside of the heat shield. Heat conduction is based on temperature difference and time[1] and the conduction of the material[2]. Since the heat shield tiles have a very low thermal conductivity, it takes a long time for significant heat to pass through.

Yes a more aggressive approach will lead to a greater temperature, but it'll also provide significantly greater drag, thus the the extreme temperatures only exist for a relatively short amount of time, and thus it doesn't have time to pass through the tiles and heat up the inside.

A very shallow approach has significantly less drag, and you spend significantly longer slowing down. The temperatures might be a fair bit less, but the much longer time spent decelerating means it has a chance to make it through the heat shield tiles.

It's not entirely unlike iron meteorites which can still be cold when landing, as they only spend a brief time in the atmosphere[3] and thus don't have time to heat up.

[1]: https://en.wikipedia.org/wiki/Heat_equation#Interpretation

[2]: https://en.wikipedia.org/wiki/Thermal_conductivity_and_resis...

[3]: https://earthscience.stackexchange.com/questions/127/what-te...