Dilex is a good solution if the color closely matches the tile. If it doesn't, it's much too "look at me". A good grade of silicon caulk, done properly, should be fine for years and years.

I understand your thinking, you want a permanent solution, and caulk requires maintenance, but in my opinion that’s not going to look great. If you want to use the cove, consider black that will match your absolute black counter material. Your counter and tile installers will need to know ahead of time that you are planning to use it.

With your new installation, perhaps consider making sure the caulk space between the counter and backsplash is the correct size, then take @Minardi’s suggestion to use a better quality caulk, seal and maintain it. Good luck with the reno!

Decent caulk please, match the counter. Don't buy ugly.

Dilex is the modern anser to this issue but IMO best when it blends into the background so maybe check with samples to see how it works in your space For me it would add two more places for cleaning since now you will have 2 edges that have to cleaned .