Pull the gutters and install rainhandlers.

"install rainhandlers."

I'd be interested in hearing others' experience with those. I'd expect them to be less than ideal for anyone who has cellar dampness problems. Most of us with cellars need downspouts that discharge the rainwater well away from the foundation, and those gadgets don't look like they'd do anything of the sort. They also cost significantly more than normal gutters from the home center.

As for your roof's appearance, I'm undecided too. At first glance I thought that they sort of make the porch shrink under its roof. However, they're interesting and distinctive. I'm on the fence.

If that were my house, my thought would be that they're more effort to change than to leave alone, and that would be the deciding factor. :)

That is such an interesting detail it would be a shame to lose it. Have you looked at larger gutters- ie if yours are currently 4” get 6”. Alternatively flash the tops of the horizontal parts before installing the gutter

I would avoid gutters as long as there is a way to control water and keep it controlled around the base of the house. Read these pearls of wisdom.

https://www.finehomebuilding.com/forum/stop-me-from-putting-gutters-in-ground