It's pretty obvious the SP-FX Team threw in the turbolift sequence as a bit of fun and to add some excitement to the eventual chase scene with Booker.
I don't think it's any worse than Riker and the Viceroy fighting over a bottomless pit in the bottom of the Enterprise-E secondary hull in "NEMESIS".
Most folks just go with the flow and enjoy the scene for what it's worth with Riker/Booker eventually defeating the Bad Guy.
I don't mind in in latter "post Doctor Who TARDIS tech we saw in Enterprise" Discovery. In Q&A however...