Why isn't forcing users to accept new Terms of Service by threatening
financial loss, (like denying access to purchased content, or
inhibiting or prohibiting the ability to earn an income), considered
extortion and therefore illegal?
Usually this is not illegal, and even if it is, it usually doesn't constitute extortion (or extortion's civil counterpart, which is called "duress", which is an affirmative defense to contract enforcement).
Generally speaking, exercising a legal right someone already has, for a purpose that is not improper, does not constitute extortion.
A TOS Rarely Creates A Reasonable Expectation That It Won't Change
Most importantly, in the case of terms of service governed information technology services, the firm that creates the terms of service reserves, at the outset, the right to change them at any time.
So, the user has no reasonable expectation that the terms of service won't change in a manner that they dislike. There is no implied promise to never change anything material about the service.
Terms of service are usually specifically drafted from the outset to avoid creating something that looks like a property interest on the part of the user in having the service continue to work in a particular manner.
TOS Terms May Not Be Unconscionable
Both the original terms of service and any subsequent amendment of them, is not permitted to be "unconscionable" (e.g. it can't make the life of your first born child a liquidated damages provision that applies if the terms of service are breached).
But, there isn't much of a legally protected reliance interest in not having the terms of service changed in this situation (although almost every general rule could conceivably have some exception to it, probably far more factually extreme than the fact patterns identified in the question).
If a term is unconscionable, it may not be enforced as contrary to public policy, without regard to what prior versions of the same agreement may have stated.
TOS Changes Are Usually Prospective Only
On the other hand, a terms of service amendment is generally only effective prospectively and does not generally change rights that have fully accrued and vested prior to their amendment, at least until the user takes some act to affirmatively continue to use the service going forward.
When there are vested rights under old versions, the remedy is not to characterize the change as extortion, however. It is to not apply the amendment to the terms of service retroactively to the already vested rights.
For example, if the old terms of service did not contain an arbitration clause, and litigation was in progress under the old terms based upon old transactions, and then a new terms of service were adopted that mandated arbitration, this amendment would not generally be applied to require the pending lawsuit in court to be stayed and transferred to an arbitration forum. The right to litigated vested when the lawsuit was filed.