No, it's not fumes since there is LESS chlorine evaporation when the active chlorine level is lower. When you don't use any CYA at all, then the active chlorine level is higher unless you maintain a quite low FC level. That's what DIN 19643 does in Europe -- it specifies a 0.3 to 0.6 ppm FC level with no CYA (0.2 to 0.5 ppm FC if ozone is used) but that's not the minimum in the U.S. where it's usually 1 ppm FC minimum in most states and in some places it's higher. For a high bather-load pool, you need a higher FC to not run out locally unless you have outstanding circulation. With CYA, it acts as a chlorine buffer so can hold chlorine to be released anywhere in the pool quickly.

The only downside to having a small amount of CYA indoors is that the lower active chlorine level means slower oxidation rates so it really becomes important to use supplemental oxidation system, but the plus is that this will lessen chlorinated disinfection by-products.

Specifically PoolDoc says the following about CYA use in indoor pools in this link:
And, you don't need to stabilize indoor pools: there's no sun inside (well, hardly any). Actually, there may be a reason to use small amounts of stabilizer on some indoor pools, but I'm still testing this. If you are having operational problems on an heavily loaded indoor pool -- residential or commercial -- and are ALREADY following the other recommendations on this page, contact me.
and in this link he says the following:
Well, why not just run LOW chlorine levels without stabilizer?
On indoor pools, with no exposure to sunlight, that's definitely an option.

But on outdoor pools, chlorine's half-life without stabilizer can be as little as 30 minutes under full so. This means that if you have 1 ppm at noon, you'll have 0.5 ppm at 12:30 and 0.25 ppm. To keep a pool safe under those conditions means that you have (1) add chlorine continuously, and (2) have a really good circulation system that is running 24/7.

It also turns out you have to be willing to use a lot more chlorine than you would otherwise.

So stabilizer is necessary for good sanitation?
Yep.

Without stabilizer, everything has to be pretty much perfect in order to maintain a santized and algae free pool. Years ago, commercial pool were operated with chlorine gas, soda ash, and not much more. There were a lot of cloudy, stinky public pools!

Swimming pools are enough work, even when done right. The BBB Method is ALL about not making it worse by adding stuff you don't need.
In this link he says the following, but that's mostly referring to higher CYA levels typical of using Trichlor indoors, not low levels such as 4 ppm FC with 20 ppm CYA:
Stabilizer (on indoor pools) -
Stabilizer (conditioner, cyanuric acid, isocyanuric acid) is only useful if your pool is exposed to sunlight. Indoors, it does nothing for you, and can make things much worse.