It might be tempting to suppose that, because MT ascribes 73 psalms to David and the LXX 84, there was a tendency to add ascriptions to David to the psalms.
I would like to speculate about a contrary tendency to remove authorship ascriptions. The particular piece of evidence I would adduce for this comes from the ‘Psalms of Ascents’.
In MT these psalms share the title שיר המעלות 'song of the ascents', except Ps. 121, which reads שיר למעלות 'song to/for the ascents', by the simple change of one letter. Further ascriptions of authorship to David (122, 124, 131, 133) have been arranged more or less symmetrically either side of the central psalm 127, which is ascribed to Solomon. On either side of Ps. 127 the tetragrammaton occurs 24 times (I think this observation goes back to Hengstenberg).
However, this careful arrangement may have been produced by removing ascriptions to authors. The unusual structure שיר למעלות in Ps. 121 is the clue. In the Qumran text 11Qpsa we have a lacuna just at the beginning of Ps. 123 followed by דויד למעלות 'David to/for the ascents'. The lacuna is most naturally filled by the word שיר 'song'. Thus the whole title would read שיר דויד למעלות 'song of David for the ascents'. The use of the preposition lamedh 'to/for' is clearly necessitated by the fact that the construct-genitive relationship cannot be used here: 'song of David of the ascents' is not possible.
Thus it seems that MT's 'song for the ascents' in the title of Ps. 121 is a structure that can best be explained by the existence of an earlier authorship ascription. Of course, it is not possible to know what name may have been there previously. As often, MT suggests a previous history, but does not allow us to identify what that history is.
This, alongside the obscurity of information within the titles, would be another argument for some antiquity to traditions of information that formed the titles.