i-size (more so the new standard R129) was launched in 2013, it took a few years for seat models to filter onto the market, but I'd say yes, it probably had a lot to do with it, partially because the majority of i-size seats which replaced the old "Group 1" (the 9-18kg / 9 months to 4 years category) were spin seats or modular base inserts which had the ability to rear face up to roughly age 4. Practically, most people find this size of seat is too cramped to continue rear facing past about age 2, but it certainly got people past the first hump which was assuming only infant carriers could rear face, and the second hump which was assuming a "normal" age to forward face was about 9 months (or ability to sit up) which had been the prevailing wisdom basically since car seats were first invented, at least outside of Sweden/Norway.
The other positive impact that R129 had was the focus on the lower age restriction against forward facing before 15 months and the resulting marketing campaigns promoting the value of longer rear facing. Because this was a significant jump up from 9 months it changed people's behaviour. I remember reading that there was some disagreement in the regulating body around where exactly to set this limit. The US was having a shift at the time where many states had raised the minimum age to FF to 2 instead of 1 year, after an influential study claiming up to age 2, rear facing is 5x safer (which was later retracted). Swedish road safety authorities and various European studies pointed to 4 years as the milestone, and wanted the full 105cm. Business was against this as felt consumers would not go for it - ERF was not popular with manufacturers at the time.
But anyway, I think the fact that it was 15 months was helpful in terms of the fact that most infant carriers despite their marketing don't practically last all the way to 15 months, so when choosing the second seat parents are forced to look for options which include a rear facing feature, and then the fact they're faced with all this choice, literally dozens of models which can rear face all the way up to 105cm (or longer) whereas previously there were a couple of seats like Britax First Class, which did RF up to 13kg/FF 18kg or the little-known and expensive Swedish imports, but over 90% of the seats on the market, including everything with any interesting features at all, were forward facing only.
When you've moved to a second stage seat that can stay rear facing then often people do just carry on a bit longer. Some people ignore it completely of course. Some switch on the 15 month mark ASAP because they misunderstand the rule or just prefer it or don't know that there's a continued safety benefit, but a reasonable proportion of parents (about a quarter, which surprised me) continue to RF up to about age 2-3.
Another market shift which had happened a few years previously also inadvertantly helped - when the law changed to require the use of boosters up to age 12 rather than them having been optional previously, there was quite a big explosion in the number of the "Group 1-2-3" type seats which converted from forward facing harness seat to high backed booster (and sometimes further to a backless booster). Previously there had really only been two types of car seat - the RF carry type for young babies, and the FF Group 1 seat. Of course booster seats too, but they were always optional. When the law came in to enforce booster use, parents didn't like the fact they felt they were being forced to "keep buying seats" so the introduction of an all-in-one from 9 months to 12 years returned things to the previous status quo and they were really popular.
However - Phase 1 of the roll out of R129 did not cover them. The first stage which started in 2013 covered only i-size compliant seats, meaning they had to be fully isofix and up to a maximum of 105cm. 123 type seats include a high backed booster stage, which was only included in the regulation in the second phase which was rolled out in 2017. You could still buy 123 seats in 2013-2016 but they were all R44 so they were less attractive than the shiny newer R129 seats, and mostly popular either at the extremely low budget end of the market, or among parents of older children who needed to vacate the spin seat for a younger sibling to move into it.
The very first spin seats including a RF mode (original Cybex Sirona and Britax Dualfix) were not R129 and neither were any of Joie's original cheap RF seats (Stages/Tilt/Steadi) even though they launched in 2013 as well. So I do think to some extent, the market was going this way anyway regardless of R129. But R129 and i-size definitely helped, yes.