I think the notion that 'clean' assets can be frozen pre-trial is unfair, but as long as a public defender is actually available, that would seem to satisfy the amendment.
I could possibly see the spirit of the amendment better served if everyone were defended via the same public-defender system, regardless of income level. That would provide equal access to justice, and also provide middle-class and wealthy people an incentive to make sure it's actually properly funded, since it's the system that would defend them, not only poor people. I'm not sure if that's a better or worse interpretation of the letter of the constitution, though.
There are still limitations. E.g. someone going private could hire a team to spend whatever time necessary while someone being defended under the public system will get one lawyer subject to billing limitations. And people relying on the public system does not get to pick and choose. But at least you have a good shot at getting someone good, that is not overloaded with cases.
As an example, I was sued by the government for refusing to accept formalities around my refusal to accept conscription (a small number of people go to jail in Norway for it every now and again for 3 months or so, and they keep making the accepted reasons to get out of it more lenient to make people just pick one of the accepted reasons rather than make a point; for my part it was very much to make a point, though I didn't end up in jail in the end), and my government appointed defence lawyer was one of the top lawyers in the country, who had argued cases in front of the Supreme Court multiple times, and who had conscription related cases as a special interest.
It's quite tragicomic to me that left-wing Norway has privatized the public defender system exactly to provide more equal access, while the US hold on to a socialized system that practically guarantees unequal access to justice.
Define "actually available"
Most public defenders offices are so oversubscribed and underfunded that they can't really provide good representation for the majority of their clients.
The current case seems to be arguing something different: that freezing defendant's assets that they could use to pay for counsel is a 6th amendment violation even assuming an effective public-defender system. That requires a separate right, something like: the right to pay for the best defense you can afford. Afaict, this is at the Supreme Court because they've never ruled either way on whether the 6th amendment includes such a right; the previous cases have focused on the minimum threshold for what constitutes effective assistance of counsel.
(Note that the standard requires both that your counsel was ineffective, and that his/her ineffectiveness caused your conviction)