Hi there,
While this would be a fun feature for those with the SkyWars, EggWars, or Plus subscription/rank, you have to think of the bigger picture. If there are 50 or so matches running at the same time (and that's only for one gamemode), and let's say there's about 40 players online with the SkyWars Rank (Bedrock as an example). If all of them are in a private match, there would need to be nearly twice as many matches happening, which could cause lag, especially with quick-transfers. CubeCraft would also need a lot more servers to route players into the matches.
However, if you do want to PvP your friend, I don't see why you can't do so in your own world. I would highly recommend downloading one of CubeCraft's survival spawns (such as Candy Kingdom) to do so.
Thanks for your suggestion, but I don't think this would be realistic :).