Why should melee weapon users get their means to inflict elemental damage for free while Destruction magic users have to expend magicka energy?
If the only way mages had to regenerate their Magicka was by consuming filled soul gems then this might be closer to a fair comparison.
Generally in RPGs part of the balancing factor for this is in the usage: melee weapon users must by definition be in melee range to deal their damage and can
typically strike only a single target at a time, whereas a magic user can work from range and can affect a large area simultaneously. You don't see for example D&D's Longsword+1 needing charges to maintain; not even if it's a Fiery Longsword + 1. Of course, magic is also (ahem) "somewhat" more powerful in D&D, the balancing act there is very different, but the point remains - regardless of resource costs, a melee user's damage is
never "free", it comes with the "costs" associated with getting into and staying in melee range.
Even if you are convinced that additionally, a charges system is right for balance in TES/Skyrim, I'd be very surprised to see anyone argue that the current soulgem system was anywhere close to ideal. The existing system is chock full of "busywork" chores - like the sort of inventory management that's necessary for efficient soul capture if you
aren't using this mod, and I think that's really where complaints stem from. I don't believe that "player inconvenience" is the right path to go down for balancing, not as the exclusive method anyway.
There's other elements of the game's design that interact with this too. In Skyrim, it is trivially possible for Destruction magic users to gear to make their destruction casts free. Melee weapon users will always need a steady diet of souls to keep their weapons charged. As I alluded to at the start, Magicka also regenerates passively over time, whereas charging an enchanted weapon is a manual, multistep process. A bigger problem (imho) is that non-magical weaponry can be improved via smithing to a point where it overshadows any damage possible by Destruction magic. The simple comparison falls apart when you start looking at the details.
I'd love to be able to round this post out with my suggestion for improving the system but I'm not there yet. This mod is a great start though.