"New Battle" mode, as I understand it, was created more for testing purposes. But nevertheless, it is also convenient and just to test different tactics. But there are a few disadvantages.
First - you have to play a random set of soldiers. This of course is also useful, but it would be nice to use the same soldiers that have already trained in the main game. You're already used to them, you know their strengths and weaknesses. You could try how useful they are against some specific enemies in certain missions.
Second - the content of the file battle.cfg, which contains data for the "New Battle", does not depend on the inclusion and disabling of mods. But even simple mods (not like X-Piratez) can greatly change the parameters and soldiers and their enemies. And then the soldiers created for the vanilla game can be weak against strong enemies from the included later mods. In this case, have to manually delete the file battle.cfg, so it was created anew, with the included mod. And so with any major changes.
Third - there is at least one mod (XCOM Multimod), which is not quite properly defined new classes of soldiers and it leads to the creation of the "New Battle" soldiers with unusable for battles statistics. Whereas in the simple game with the mod, this is not observed.
Hence my suggestion - to give the player an opportunity in a mode "New Battle" to load from any individual normal saving section "soldiers" in the file battle.cfg, replacing the previously used for "New Battle" soldiers. This will allow you to quickly add the already familiar soldiers to the "New Battle", where you can check them in all available in this mode missions.
It is possible to do this manually, although not so easy. I tried it by moving eight rookies from the very beginning of the vanilla UFO game to the battle.cfg file (replacing the rather diverse troops that were there). After which they appeared in the "New Battle" as soldiers to choose from.
If this is added, it will even be possible to fight against aliens even with soldiers from the already completed game, just using them in "New Battle" mode. It's too early for them to retire!
And playing with the new mods will allow you to quickly add new soldiers to "New Battle" to test just with the new mods included.
Additional suggestion:
This is already more complicated, but it would also be nice to move the base map from the usual save in battle.cfg as well. The one that is usually used in the "New Battle" is quite primitive, because it is the starting base. Therefore, testing the mission "Defending the base" comes out rather monotonous.
And loading an already developed base from the usual save can diversify the process.
But here is where the difficulty is foreseen. There can be up to eight bases in a regular save, whereas in "New Battle" only one base is always used. But at least moving the very first base from the general list would give a lot of new possibilities.
If the text is not clear everywhere... I'm sorry... Machine translation.