Do you feel this to be a problem?
If so, what to do about it?
Not a problem as such, but I don't find either option fully satisfactory.
First of all it should be noted that (a) weaponry and (b) accessories are very different things! Weaponry choices are obviously tied to your PC's combat capabilities, and is more important than anything else in equipment, as it determines your fighting style and effectiveness. Accessories are mostly for the exploration pillar of the game; they are the kind of things that are easy to overlook, and later regret when you wish you had a longer rope, more torches, or other tools...
Rolling wealth and then pick equipment manually is IMHO one of the most boring things in the whole game... not because of the weaponry but because of the accessories. If you use this as a default, IMXP the players spend too much time reading the whole equipment table and descriptions, and find too many little inexpensive tools that "could be useful, eventually". It really slows down the first session, and since I always have more first sessions than second sessions, I really appreciate the various "packs" in 5e as well as the background's packages.
OTOH fixed weapons and armors aren't good, even if you get multiple options. They are still more complicated than needed with no sensible balancing factor, and still forbid some combinations that might be essential for a character. And it's all pointless because after the first treasure, they can fix these deficiencies.
I'd rather base the starting weaponry on a PC's
proficiencies. For example:
- You get
three weapons you're proficient at
- You get
one shield IF you're proficient in shields
- You get
one armor you're proficient in, or none if you're not
- You get each tool you are proficient in, if any
Three weapons is enough to cover melee+range and 2WF.
Optionally, you can still set individual cost limits (e.g. armor max 100gp) or total limits (e.g. total max 200gp), if you're worried.
- In addition, you still get the other class-based equipment (e.g. spellcasting tools, packs) normally, as well as the background equipment.