If I am playing a spellcaster or martial artist, spell slots and ki points represent daily powers my character can use. Keeping track of how much I have left does require some minor bookkeeping, but I know that if I can make it to the next long rest I will get all or most of that power back, which is reassuring.
Whereas fragile weapons would not recharge after any amount of time or rest. Warriors would start off with full power in the form of intact weapons and armor, only to begin an inevitable downward slide until the gear becomes unusable, at which point the only thing to do is go find new gear so the whole dreary cycle can repeat itself. It would be an inescapable loop of negative reinforcement, as opposed to the positive reinforcement that wizards or monks get after resting.
If weapons are extremely breakable, any slightly better weapons will likely be treated just like magic consumables. I think we have all seen players hoard potions for a rainy day that never comes. These items become dead weight and the DM might as well not even give them out. Lower quality weapons will be used up and thrown away, and play will likely devolve into a slog of endless scrounging for more weapons.
Early editions of D&D tried to nerf spellcasters with material components, which were usually consumed. Mages needed all kinds of weird, gross, or expensive stuff in order to cast most spells, and if the DM required the search for components to be played out I can see this wasting a fair amount of table time. Druids had to harvest mistletoe with a gold or silver sickle under the full moon if they wanted to cast at full efficacy. Lesser mistletoe or oak leaves could be used in a pinch, with spell power diminished in various ways, but in effect a druid player with a strict DM had to stay near oak woodlands infested with mistletoe or else risk losing spells altogether. No desert or polar adventures for 1E RAW druids, let alone plane-hopping! Material components are one of the most disregarded rules in all editions of D&D, and fragile weapons seem a lot like “spell components for fighters” to me.
I actually think that some form of weapon breakage is not necessarily a bad idea, but it should be rare and dramatic or else it would become a nuisance. Gear maintenance should be assumed as part of a warrior’s routine, not something to be played out at the table.
If the goal is to encourage tactical thinking, then giving weapons slight buffs and debuffs under various circumstances would be a much better way to do that. 1E had a crude version of this in the form of the weapon vs. armor table, another often-ignored rule which required constant reference to a huge table of all weapons. When I ran 2E I used the optional weapon type rule, which was a much simpler way to achieve the same result. Weapons were either slashing (S), piercing (P), or bludgeoning (B), with a minor plus or minus against various armors listed on a much smaller chart. Some monsters like skeletons were weak against some types and strong against others, which introduced a rock / paper / scissors dynamic that I found to be fairly intuitive. Some weapons might be too big to use in confined spaces, and I like having some way to determine when and where missile weapons can be used.
The heroic focus on special weapons has roots in mythology and medieval legends, with Arthur’s Excalibur or Roland’s Durendal being treated almost like characters in their own right. In early editions of D&D the use of magic swords appears to have been a stealth class ability for fighters (not actually pointed out or explained in the rules of course...

), which was only reinforced by EGG giving AD&D swords the almost unique ability to do more damage to Large size foes, instead of less. If we want to encourage players to switch up their weapon use then I would favor the carrot over the stick.