Baron Saarthuran von Gushiddan:
If everyone's holdings were insolvent, the Imperium would be insolvent. Even the percentage of PC nobles that have holdings but never see/use/run them would be an indicator that large parts of the Imperium were not working.
Your observation is completely true, Your Excellency, and completely inapplicable. While I have run campaigns in which the PCs attain great wealth - hundreds of billions of Imperial Credits' INCOME, mind you - these are usually endgame scenarios. Planetary noble-scale monetary resources at start-game are likely to cause campaign-threatening problems.
On to the "rules," as shown in T20; they're more generous with starting money for the noble than CT or MT.
A noble ending Prior History has access to significant wealth only if they own a yacht at least 25% (i.e., they get "yacht" as a mustering out benefit at least twice, once for the down payment and once for 25% of the payments). They can sell the yacht for a few-to-a-dozen MCr and have all the non-starship-purchasing money they're likely to need, unless they're going to do something like outfit a grav-tank mercenary company.
Other than that, the noble ends up with an MCr or so at best, and if they went enough terms, another MCr 0.12 per year (10k/month) for a "pension."
With their big social standing, they can also use a class feat (Trust Fund) to borrow more money, of course: a noble character with an 18 SS can borrow MCr 18 versus an 8th level char with Credit Line and an 8 SS, who can borrow only 64,000.
So the noble might have a million, some of it borrowed using Credit Line, if he rolls really really well, liquidates some of his mustering out benefits (remember, he can only take three rolls on the money table), and takes a loan. He can draw on his title's Trust Fund,
if he has established credit patterns, so not at campaign start, for SS x 1 MCr as a loan.
That's it, and setting aside the Trust Fund loan for a starting character, maybe a million, tops, with Cr 10k/month and another Cr 200 x SS, let's say 3600/month, for a total of Cr 13,600/month income. There is no provision for this example Baronial character to get access to more money within the rules.
Even someone who gets up to Duke in the Prior History is going to have little more money - they can borrow a little more with the Credit Line feat - but will eventually be able to borrow more against their Trust Fund.
So
quod erat demonstrandum, a Traveller noble
player character cannot, for whatever reason, draw significantly on their ennobled wealth unless the GM bends the rules in some way.
Which implies that either the PC is not the inheriting noble (older siblings), there are constraints (perhaps Constitutional) on how much of their peoples' money they can spend, or other restrictions. These restrictions aren't stated anywhere, so they aren't canon, per se, but they are there.
<Traveller-speak>Respectfully Submitted For Your Excellency's Consideration</Traveller-speak>