Is ghusl required upon the emission of semen merely through thought, without differentiating whether its emission is with desire or without desire, and in light of suffering from frequent ghusl and the resulting illness, and deprivation from reciting the Quran and praying?

The liquid that usually exits is madhiy (pre-seminal fluid), which is discharged when thinking about sexual desire. Its purification involves washing whatever it has touched on the body and clothes.

If you are certain that it is maniy (seminal fluid), then ritual bathing (ghusl) is obligatory by consensus if it exits with desire. However, the Shafi'is obligate ghusl upon the exit of maniy absolutely, whether with desire or not.

If you are in doubt whether the exiting fluid is maniy or madhiy, you have the choice of considering it maniy and performing ghusl, or considering it madhiy and washing the affected area and performing ablution (wudu'). The latter is the fatwa we adopt.