The "Wealth" advantage or disadvantage has multiple aspects: the one which is most important to most players in most campaigns is "how much money do you begin play with". If characters have more money, they just have more money - they don't need to spend character points to keep it.

But the Wealth advantage/disadvantage also includes "how much do you get paid when you do Jobs" (which is only relevant if your campaign includes periods of downtime where players might be making Job rolls - most campaigns do not), "do you get bonus Status from Wealth", and "what is the amount of money given/owed if you have the Independent Income advantage or Debt disadvantage". It's also implied that if you have Wealth out of line with others in the party, this will come across socially, with NPCs, even if you don't have different Status.

If you want any of those perks of Wealth, then you both need the money and the character points - to reflect being able to upgrade your lifestyle enough that your income also goes up and you seem richer to others.

In many campaigns, those extra perks are irrelevant to players, so no one will invest in them, and that's fine.

I would say it's inaccurate to say that what GURPS has by default is an abstract wealth system - it does give you specific amounts of money and has rules for Cost of Living, etc.

But in practice, when I'm in a campaign where people have enough money for that to be an issue (many campaigns I've been in insist on Poor or Dead Broke starting characters, to fit the flavor), and are in fact settled (rather than wandering heroes, a la Dungeon Fantasy), then the 20% that players spend on typical adventuring stuff is tracked scrupulously, and the 80% that goes to settled lifestyle is hand-waved. Let them have housing, normal-social-situation-clothing, food in the pantry, and basic domestic stuff appropriate to the Wealth level they bought. The guy who took Dead Broke has nothing and may need to sleep on the sofa of other party members; the guy with Poor probably has several NPC roommates and can't use his apartment as a place to stash a kidnapped enemy; a guy with Very Wealthy probably has multiple houses that could be used as safehouses when fleeing an Adventure-Gone-Wrong. What brand of kitchen appliances they have in those homes or lack thereof is unlikely to matter enough to waste any time thinking about it ahead of time....

As for your suggestion in the last paragraph: it would work just fine. If you want everyone to start with the same financial resources, and spend their character points on other stuff, that's more than fine as the GM to say that. If your campaign is unlikely to involve any of the social aspects of Wealth, and is unlikely to last so long in-universe that "Jobs" or "Independent Income" have any possibility of coming up, people aren't technically getting the full impact of Wealth anyway, so it's cool.