The missing factor is that FIDE took control of the World Championship title in 1946, and implemented a regular cycle of Zonal tournaments, Interzonal tournaments, candidates tournaments to determine a challenger to the existing Word Champion starting in 1949/1950. (The candidates tournament was changed to candidates matches after 1963 - see Bobby Fischer's complaint "The Russians have fixed World Chess": http://sportsillustrated.cnn.com/vault/article/magazine/MAG1... )

Before the war, major chess tournaments were sponsored by wealthy chess patrons. FIDE represented amateur chess players, I think their crowning achievement was their nomination of the Max Euwe (who described himself as an amateur, he was a full-time teacher) as Alekhine's challenger in 1935 (and consequently beat Alekhine and became the 6th World Champion). FIDE had no hold over top-level chess. (Edit: FIDE also suggested Bogolyubov as Alekhine's challenger, twice. In all cases FIDE could not force Alekhine to accept, but Alekhine did accept to these challenges - possibly for financial necessity)

FIDE's World Championship cycles from 1949 onwards greatly increased the number of chess tournaments titled players could participate in, globally. Particularly the Zonal and Interzonal tournaments, brought together thousands of chess players regularly in - at the start - 3 year cycles.

So immediately, the number of tournaments involving titled players that adhered to FIDE rules jumped up substantially, and since the World Chess Championship cycle became the main top-tier events, other chess events naturally standardised on FIDE rules, and gave rise to hundreds of FIDE-rules tournaments.

So yes, the removing of the short-draw avoidance rule, in the context of a massive and new qualification cycle for the World Championship title gave rise to the side effect of shorter games.

Before the war, in patron sponsored top-level chess tournaments, each tournament had it's own set of playing rules. They were generally the same, a modification here and there based on previous tournament experiences of sponsors and influential players. There wasn't a consistent set of rules (until FIDE in 1946). For instance, in the Nottingham 1936 tournament book by Alekhine, he writes that they dropped the no-short-draw rules because it was becoming more evident players were circumventing that rule anyway, so it wasn't stopping non-competitive games from happening.

And the World Championship matches were predominantly decided by the current title holder, and mostly about whether it was financially worthwhile to the title holder to risk his title on a match with a sponsored challenger.

In turn, I wonder whether the tailing off of that in 1970 was the introduction of the Elo rating system and the Fischer-effect leading to the professionalisation, financial viability and the commercialisation of chess?

Maybe a rating system infused more competitiveness into tournaments, more professional application from the players.

Also, the tailing off of game length happened right when Fischer returned to the qualification cycle, where his spectacular series of results culminated in winning the World Championship in 1972 against Spassky in Reykjavik, starting the fracturing of the Russian hegemony of World chess.

Fischer also pushed for chess professionalism from a commercial/financial point of view. More money started to flow into chess because of Fischer and his financial demands / quality expectations. Perhaps that started the conversion of chess from a state-run Russian-owned speciality to a commercial/sponsored prestigious tournaments (e.g. Montreal 1979, San Antonio 1972, Milan 1975). And in conjunction with a rating system, compelled players to be more motivated towards playing for the full point, to improve their international standings, to improve the quality of tournament invitations, leading to more financial stability.

Somewhere between the Russian dominance of the World Chess Championship, up to Spassky losing to Fischer in 1972, and the multi-million dollar Kasparov-Kasparov matches from 1985 onwards, elite chess became a financially enriching career path for more and more players. 1970 may have predicated that, and the gradual rise of the length of games a side-effect of money being pumped into chess and initially the Fischer-effect.