Eh... the weight of the warhammer and the cheaper price of the battleaxe are such minor benefits in my experience (I see very few games where encumbrance is calculated and starting gold is at such a premium that the 5GP difference would actually affect purchasing decisions) that balancing out the weapons as purely an aesthetic choice is probably due.
As far as the reduction of elves using longswords in 5E... it really comes down to that niggling +1 bonus to hit and damage you get by players choosing to steer into the elves' +2 DEX racial feature inspiring them to go DEX-based rather than STR-based more often... and thus choose the rapier instead. So I can understand perhaps the "loss" of more longsword-focused elves in 5E and the chagrin that could cause amongst the playerbase... but at the same time I also recognize that both weapons do 1d8 damage, so what *really* is the difference here, other than our own preconceived visuals of what the weapons look like? Yeah, when we see the term 'rapier' our minds immediately go to fencing swords, whereas the term 'longsword' evokes the wider blade weapon of medieval combat. But who's to say that for elven culture... that due to the size, weight, and physicality of elves in comparison to humans, that a longsword an elf would design might actually look and feel more like a rapier in the hands of a human? So that the weapon in the Equipment chart that has that Finesse property (and thus perhaps more likely to be picked up by an elf) is actually *to them*, a longsword. And that what a human would call a longsword perhaps might be considered a 'broadsword' to an elf (due to how wide the blade was.)
Who's to say? I mean, it all comes down really to arbitrary words selected to be used on the Equipment chart to describe all manner of weapon, regardless of how accurate those words actually are. So since there's no damage difference between them... why not consider the human rapier to be an elven longsword in your own mind? As I've been generating a bladesinger type of elf character for a potential campaign... this is exactly the kind of thing I've been wrestling with. And I finally came to the conclusion that 1d8 is 1d8, so who cares the word that the book uses as a weapon identifier? If my bladesinger's blade is a "rapier-like" longsword (because I end up choosing to finesse)... then so be it. The character is still going to be all-focused on a bladed weapon, regardless of the name used to describe it.