Alright, I just did some digging to see what the specifics were. The answer is a bit complex: there has always been a transportation budget for the various conveyances, but managed very differently through the years. But let's go back a bit farther. In the early 60s, Walt and Roy were talking about how to improve communities of the future, which was where the seeds of EPCOT started. Walt Disney Productions had a bunch of different divisions, and in the mid 60s, one of the ideas from Imagineering and Walt and Roy was to try to sell communities on better transportation systems, which could be - of course - built and sold by Disney. In 1974, a division of WDP was created to market and sell those transportation systems to cities, namely WEDway's and Monorails. That division was called Community Transportation Systems, fully owned by WDP. CTS's only project ended up being the Houston Intercontinental Airport's WEDway PeopleMover, sadly. The plan was to use them in cities around the world, along with the rest of the WDW property, including EPCOT, but none of this came to pass.
Now, the monorails and trains in the parks were licensed by Retlaw, which is a different company, but also owned by the Disney's. Disney the company paid Retlaw fees towards the monorails. Disney the company also had a transportation budget that was allocated towards monorails, ferryboats and other transportation needs. Those budgets were more than enough to cover what needed to be covered.
In 1981, CTS, while finishing installation in Houston, was renamed WED Transportation Systems. In late 1981, they folded WED Transportation systems into the corporate structure as part of the same deal that moved licensing and ownership of certain IP and the track-based attractions from Retlaw to Disney. That's when you start to see the language of ".25 of this ticket goes towards transportation" on the tickets. Prior, Disney had sold separate transportation tickets folded in as part of the entry books or resort stays through the 70s (with a portion of the ticket book price supporting transport), then there was short period of no mention of transportation aside from needing a hand stamp to utilize transportation if you were leaving the park, prior to the fee language appearing in '81. The language was on the tickets through the mid 90s when the ticket media changed over again.
I don't know when the transportation budgets were re-aligned, but I suspect it was in the early to mid 90s also as part of the management changes during the time, independent of the language being removed from the ticket media. I believe WED Transportation Systems still exists today as a corporate entity, though.