Even a lot of modern sampling hardware works that way.
The only samplers I use which truly have 'on-the-fly' recording and playback are my Octatrack and some Eurorack samplers. I do use the heck out of those features.
The Octatrack in particular is a lot of fun in that regard because the record functions can be sequenced. So if I have a sequence playing back while I'm playing guitar or something, the OT can be programmed to record a loop and then start playing that loop when the next pattern is launched. It's crazy flexible.
I think it would be difficult to achieve that kind of thing without putting a dedicated sequencer into the Sampler but that kind of thing can be done with the clip launcher.