It would probabl help to reduce the locals going up-canyon but won't impact many of the tourists. The toll would just be built into the travel expenses and is relatively small in comparison to the total trip cost.
I doubt a $20 to $30 per day toll is going to discourage a local BCC/LCC rider/skier from hitting the slopes on a powder day, especially given the long history of what many do to beat the canyon closure for control work and the strategies they employ to remain hidden in the canyons until daybreak or the multitudes who rise early to park as close to the closed canyon gates as possible in the ever-lengthening line-up while sleeping, eating, surfing the Web, etc. for several hours. Other less ambitious locals will only give up their effort to get up the canyons if the line-up to do so extends x number of miles from the mouth and their vehicle hasn't made any meaningful progress for x number of hours or fractions of hours (and some of them just relocate to the other canyon line-up if they think their prospects are better there).
The article doesn't say what behavior they want to change.
From the second paragraph of the article: "The goal would be to stabilize and reduce traffic volumes by 30% through travel alternatives." The behavior UDOT wants to change is reducing the number of vehicles in BCC and LCC on the ~50 highest-usage days of the season by moving canyon users to ski buses or the gondola (or any of the other original proposals that had been under consideration, such as a cog-railroad).
What does this do to Alta's pay parking move?
I'm quite sure it does nothing because Alta will almost assuredly fill up its carparks on the 50 highest-usage days of the season in LCC. The local trend in parking fees is to add days of the week that said fee is applicable to and extend the number of weeks the program is in effect (Alta), increase the cost of a season parking pass (Solitude and Snowbird), increase the number of parking spots a season parking pass is required for (Snowbird), and increase the cost of a daily parking pass (Solitude). Given the huge increase in visitation to CC resorts, I don't see paid parking going away but instead increasing in all the aforementioned ways.