Yes, you can have both. We're getting them in our inset cabs and I've seen them in sample kitchens.

Here is a link that might be useful: soft close for inset doors

One brand I handle has them. QCCI (Quality Custom Cabinetry Inc) embeds rare earth magnets in the top and bottom of the door with aligned magnets in the rails allowing them to use soft close pistons even without the pistons they would just woosh into place. Exposed hinges are mortised instead of the wrap hinges. All standard as are 1" frames but they are pricey.
Shot a quick pick of a base I had in garage.

Christian has a slightly different (bit complicated) rare earth magnet system and Craftmaid (with a "C") might as well. Likely a few others at that price point.

I wanted both but was told this was unavailable. So we opted for soft close doors but I think I might have prioritized the hinges in retrospect and been happier.

Thanks for your comments. I initially was told that I could get soft close with my exposed hinges then I was told I cannot. For the people that have exposed hinges, do the magnetic closure on your doors drive you crazy? I am so confused right now.