I have never had that issue with a jackplug. Stuttering connection and one more thing with batteries that you need to manage. Also, most of the wireless headphones that I’ve tried have much smaller cups than the wired variety. I haven’t found a pair of wireless in-ears that are as comfortable as my preferred IEMs. In general, they might be okay for movies but not for music with an overemphasis on bass that I hate. The few options that don’t sound bad are wildly overpriced.
I haven’t purchased any cheap wireless headphones, certainly not that cheap but the wireless headphones that cost $300 sound significantly worse than a pair of wired headphones that cost half that much, sometimes even less. Same for the earbuds that sound bad and aren’t as comfortable.