The problem is still that it just plain isn’t fun to have to level up again, even if you can cut some corners by having higher level gear. (I assume you agree since you said so yourself in the last sentence).
Making amusing challenges for yourself to be able to stand playing lower difficulties isn’t a bad idea, but it is basically admitting that there is a problem, and it has no bearing on the question whether levelling in itself as-is is a good mechanic or not.
This is a very important thing, in my opinion: Just because some things work well in other games, THAT DOESN’T MEAN IT WORKS WELL IN VERMINTIDE. I must admit I don’t really know Borderlands, but from what I know of it, I am under the impression that the unending hunt for better items is a core component of that game’s gameplay loop (much like it is in games such as Diablo). (But correct me if I’m wrong, please!) That works well in such games, because the thrill of finding that rare powerful upgrade after grinding is something we humans are programmed to enjoy. But that thrill isn’t a core component of Vermintide. The thrill of Vermintide comes from improved player skill and beating a certain challenge (whether that is finally finishing a Champion run or beating DWONS is irrelevant). So in some games, like Borderlands, a levelling system and RNG loot can work really well, while still being a bad fit for other games, like Vermintide.
I find it hard to believe most totally new players will get bored after not even having finished all (boss) maps on Veteran. However, I find it very easy to believe that having to level up all over again after already playing in, say, Champion, is off-putting. A situation in which levels / hero power don’t exist, but where you have to complete a trial of competence (that can be knocked out in a single evening) would probably be infinitely better for most folks.