MS:

This is why we cannot refer to the debt as a legally enforceable obligation. The concept of natural obligation is put forward as a means of allowing discharge of a "debt" which is legally unenforceable (either because of a procedural bar such as the Statute of Limitations or because the "debt" only exists as a moral obligation such as the obligation to provide for retired parents (to borrow an example from French Law)) to be good consideration.

The Statute of Limitations does not preclude any judicial finding that the debt ever was. it is much less sophisticated in its operation. It simply precludes recovery. It does not extinguish the indebtedness, it extinguishes the cause of action to enforce the indebtedness. Why else can one simply "affirm" one's indebtedness and thereby waive one's right to rely on the time bar?

AA: i did not make myself clear i expect we will agree that the statute of limitations precludes any finding that the debt existed in the proceeding in which the running of the statute is established. such a finding would defeat one of the higher purposes of the statute, which is to preclude affirmative proofs of an obligation when time has likely eroded such contradictory evidence as the defendant might have adduced. anyway as a matter of procedure, if the running is established, the court simply has no occasion to rule on any aspect of the debt. so i wonder at your first sentence: 'that is why we cannot refer to the debt as a legally enforceable obligation': if the statute is established, we cannot refer to the debt as a 'debt'.

MS

In what other areas of law can a simple affirmation of indebtedness suffice to create a binding obligation to pay?

AA: any other time a debt is alleged by a plaintiff, and admitted by the defendant

my point was that discussions about the debt continuing, but being unenforceable simply make no contribution to understanding of the results: if the debt is denied and the statute asserted, judgment for defendant: if the statute [tho having run] is not asserted, judgment for plaintiff if there is no other defense.

what is added to legal understanding of these results by higher thought about the unenforceability but persistence of time-barred transactions??

by the way, another formulation which might pop up in american legal thought:

it is the sensible legislative intention behind the statute of limitations that it simply offers an option to the defendant to bar proof of the debt, and has no other operation with respect to the early transaction

[again a formulation which eschews the higher thought].

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i hope you are interested in these considerable differences between us in conceptualization: there are certainly many american lawyers and academics who would describe the matter as you do, but many would talk about it as i have.