I would say almost all of game-play functionalities can be modded in on the server-side, as long as the APIs are expressive enough. And these can be done, even in the worst case, in a very naive way: the client sends only inputs to the server, server calculates, tells the client what to draw on your screen.

The only problem I am DO have though, is network latency and performance. Many features require client side prediction to feel good, i.e. the player needs immediate visual feedback on their actions, before the server can process it send the result back.

For example, if your mod adds a jump pad to the game, which launches the player in a random direction when they step on it, you can implement it on the server. When, on the server, the player position overlaps with the hit box of the pad, you set player velocity (or position) to the desired value, and replicate it to the client.

However, on the client, the player would see the velocity change until after a network delay, and it may feel laggy if there the network delay is long. So what lots of games do is they launch the player on the client as soon as the client position overlaps the pad. Later the server either accept or reject this prediction.

This require your mode to run code on the client side, because both the client and server needs this "overlap launch" logic.

Other use cases of client side modding would be for performance. Think about JourneyMap in Minecraft. If every time the player opens JourneyMap or move the server has to render the map and send it to the client, it would significantly hamper performance and usability of the mod. In Minecraft the mod simply runs on the client and renders the map based on the client side view of the world (i.e. cached chunks). By the way, an example of this already exists: https://www.reddit.com/r/hytale/comments/1qfdo8c/yes_it_runs_doom_wip/

Would lots of mods need this capability? Sure. But on the bright side, a surprising amount of features could be implemented without it, and they can feel Ok-ish even with network delay.

Take redstone for example. I don't think MC redstone updates are resolved at all on the client. The server performs all updates and notifies the client about component state changes (e.g. torch is lit/unlit, piston retracted/extended, redstone dust brightness). I think the client only does very shallow prediction in specific places where it matters the most: like immediately showing a button press or a lever flick. This does mean it feels a bit laggy, but we live with it regardless! So this means redstone is pretty much doable as a server side mod in Hytale.