The amount of work your arch is doing depends on how much you’re pushing with your toes/forefoot instead of your heel. I think if you don’t have a secure heel up and have your cleat too far forward, it can cause issues with your arch.
I experimented with arch support because I would get arch pain despite having low-mid arches. I found that I basically traded one pain for another. It felt like the arch support was foam rolling my arches every time I pushed the pedals.
I also found that many orthotics increased the stack under the heel a lot, compromising the heel cup to the point of making the shoe unusable, and ironically exacerbating arch engagement.
My very uninformed opinion would be to find a shoe that totally locks in your heel, move your cleat closer to midfoot, and use as little arch support as you can.