I would say as well that the pictures of roths with 4-5+flowers are usually of selected plants from selected parents.
In the Rex x Mt Millais, there has been 5 and 6 blooms recorded, but most of the "normal" plants never produce more than 2-3 in that very same cross. Several people screened even the seedlings for that.
I have seen a bench of them in bloom in Taiwan, same cross Dou Fong x Big Garden, same greenhouse, and whilst some plants had 4-5 blooms on a first flowering, many had 1 bloom.
Apart from that, the same grower had many roths, clumps established for many years, various ones and the plants had 2-3 blooms per stem. He had a Dou Fong division with 6 flowers on a stem, 1 blooming growth and 1 new growth. He is an amazing grower ( who actually grew the famous sanderianum Shin Yi !).
There is about 75% genetics, and 25% culture.
For dianthum, there are dianthum with 4-5 flowers per stem, and they are special colonies from China ( Vietnamese and Laotian strain can make amazing clumps that never produce more than 2-3 flowers per stem). There was a very beautifully grown plant pictured on this forum, clumpy, of the Chinese strain. The plants are not always larger than the 2-flowered ones ( which in turn can have 50 cm leaves!!!).
Same for sanderianum, where many plants genetically cannot pass past 3 flower per stem. I have seen many sanderianum collected in Sarawak, and if they were the proper "strain", even a weak borderline dying plant would have 4-5 flowers per stem ( and die subsequently). For sands, I would say that the plants with long petals and/or more than 3 flowers per stem ( there are single flowered colonies as well, never more than 1 or 2 flowers, but gorgeous leaves!) are extremely rare, but extremely beautiful, that's why we see so many pictures of them. Most of the blooming size sanderianum I have seen for sale in the USA are of the 2-3 flowers per stem strain, even the so-called "select divisions". Many flasks are of that type of sand as well.
The more choicy sands are usually kept for breeding or unavailable, because the Japanese and Taiwanese are crazy about them.
Same for St Swithin, I know many huge clumps that make 2-3 flowers per stem ( especially with Charles E in the background), and first bloom with 4-5 flowers per stem, same greenhouse in the Netherlands.
Too much light can actually stunt the plant, but before reaching this point, the leaves would be much shorter and quite yellowish.
I forgot, some people "cheat" a little bit with the multis, and get an additionnal flower on the count by cutting the flower stem every other flowering. It can help a roth with 4 flowers to have 5 or 6.