There
is “plastic paper.” It was somewhat popular in the 80’s and 90’s. But I would think it would cause more problems because ink does not absorb well into the paper making it more susceptible to transfer to the film emulsion. I may be mistaken but the mottling I have experienced seems to be caused by humidity from the backing paper getting to the emulsion.
There are a bunch of potential problems that result from squishing paper with ink printing on to it into emulsions that are designed to be incredibly sensitive to small amounts of light,
And if you take steps to lower the potential for the ink to leave the paper and interact with the emulsion, you can end up increasing the potential for other things in the paper interacting with the emulsion - it always involves balance and fine tuning.
As mshchem mentions above, Eastman Kodak ("EK") and its backing paper supplier have arrived at a solution that appears to involve a type of overcoat, but you won't hear about them sharing that solution. They spent a lot of time, money and resources arriving at that solution, and they consider that solution to be a valuable trade secret.
It is important to remember that their solution has to work for C-41 and E6 colour film (and their much more complex emulsions) as well, because backing paper is so expensive, and minimum order quantities are so high, that it isn't economically feasible for them to have multiple different types made for them - at least not with the 120 volumes being as low that they are. No film manufacturer can stand having a bunch of capital tied up in a warehouse for years while one or more already paid for orders of backing paper gets slowly used up.
At the time of the EK bankruptcy, the low 120 sales volumes meant that EK had years worth of EK manufactured backing paper on hand. That is why they shut down and dismantled their own production lines.
It was several years later, when those supplies were finally exhausted, that they attempted to use third party manufactured (to modern specs) replacements, and discovered that the current paper and printing technologies they could access caused near catastrophic problems.
Not long before Eastman Kodak had their problems Ilford had similar problems with what is known as wrapper offset - transference of the ink. Ilford addressed them by making their back printing much fainter. That is why it can be so hard to see the numbers in so-called red window cameras with Ilford 120 film.