You can, of course, not use any CYA in an indoor pool or any pool not exposed to sunlight, but if you do so and don't keep the FC level extraordinarily low, then the active chlorine (hypochlorous acid) level will be much, much higher. The same regulations in some areas that prohibit or recommend against using CYA in indoor pools also have an FC minimum of at least 1 ppm. This results in the active chlorine level being over 10 times higher than in a pool with CYA that has enough FC to prevent algae growth (in outdoor pools). This higher active chlorine level oxidizes skin, hair and swimsuits faster as a result. It chemically reacts over 10 times faster to create disinfection by-products such as THMs from skin. It also outgasses chlorine faster.
The regulations on CYA only think of CYA as protecting chlorine from sunlight with little understanding of the chlorine/CYA relationship and how most of the chlorine is bound to CYA resulting in much lower active chlorine levels as a result. In Europe, especially in Germany, the commercial/public pool standard does not use CYA, but as a result they try to minimize the active chlorine level by having a lower FC range of 0.3 to 0.6 ppm if no ozone is used or 0.2 to 0.5 if ozone is used. Also note that the regulations of commercial/public pools in the U.S. do not account for the chlorine/CYA relationship even when CYA is used since they simply give ranges of FC with ranges of CYA rather than specifying an FC/CYA ratio range which would give much more consistent disinfection and oxidation rates.
It is true that a pool not exposed to sunlight will often need some form of supplemental oxidation, such as UV or ozone or non-chlorine shock (MPS), and that lowering the active chlorine level using CYA makes the oxidation rate from chlorine that much slower. So using supplemental oxidation for indoor pools makes a lot of sense. Ike, if you aren't using supplemental oxidation, then you should probably target something like 4 ppm FC with 20 ppm CYA to have a somewhat higher oxidation level and should seriously consider a supplemental system. Even those not using CYA often find problems with CC and smell in indoor pools
My wife has personally experienced the side effects of this rule where her swimsuits degrade (elasticity gets shot) and her skin is flakier and hair frizzier when using an indoor pool with 1-2 ppm FC and no CYA over the winter while in our own outdoor pool with an FC that is between 7.5% and 15% of the CYA level the swimsuits last for many seasons with no noticeable degradation and her skin and hair are not as affected by the chlorine in the pool.