Well there is no guarantee that they're done with a separate handheld system, and they've claimed that there may be a 3DS successor. So I don't think we're really in a place at this time to feel anger over there being no more dedicated Nintendo handhelds after the 3DS, as we simply don't know that is the case.
Having said that, should the 3DS truly be the end of the dedicated handheld support from Nintendo, this is what I'll miss: the glasses free 3D, the benefits that a second screen right below the top main screen brings, and the convenience of a handheld that protects itself with its clamshell design coupled with how it truly can fit in your pocket (full disclosure though, I never traveled around with my 3DS in my pocket, it was always in a case that I'd put in my backpack).
While those features will be missed (though I don't see why a future Switch successor couldn't also have built in glasses-free 3D for handhled mode, that feature doesn't necessarily have to die with the 3DS), they don't outweigh the positives of Nintendo shifting all focus to one system that can be either portable or played on your TV. If this is the route Nintendo indeed goes, it means the merging of all their great games from their handheld tier with all the great games from their console tier, which means Pokemon at home or on the go, fully 3D epic Zelda adventure on the go or at home, the reintegration of series like Fire Emblem back to the home console market while still being playable on the go. Series like Ace Attorney and Professor Layton that were only really on handheld systems (With a few exceptions) now still available there, but also on your TV. Etc. Etc. I could go on and on. Furthermore, this means your portable system has great analogue sticks and not a circle pad and C-stick nub.
Ultimately if it truly is the route Nintendo goes down, I'd be just fine with the 3DS being the end of the dedicated handheld tier from Nintendo, because the Switch (and I assume its successors) more than satisfy my handheld gaming needs as well as my home gaming needs.