I apologize in advance if this has been asked (quick search and I didn't see it) ..

Without investing any perks in the speechcraft tree, do shop owners have enough money?
ie. I imagine that towards the end of the game one can sell items that are easily worth 3000+ gold. Currently, I see no merchants that come close to having that amount of gold available.
Does the amount of gold available to merchants increase as the player-level increases?
Or is it wise to invest in the speechcraft tree for that purpose?

Merchants gold don't increase but the price of item you sell increase with speach skill level. You can either use the speech perks to increase the amount gold of any merchants or do the thieves guild quest to have fences that max out at 4000 gold.

Except for rare situations, merchants have the same amount of money throughout the game (without mods or perks). Now and then if you buy something
they will still have the increased cash available when you visit again the following day - sometimes forever - but this is a bug rather than a rule.

Other than the merchants in the Thieves guild, who increase in number (and money for Tonilia) towards the end of the questline, the only way to get merchants
more cash is speechcraft.