I don't think there is a hard and fast rule either way. It's all about trade-offs - weight, money, etc. Plus, where are you BPing and what is the weather/climate.
Personally, I approach my decision-making for gear choices based on functionality, not just weight.
While some may eschew the BT floor to reduce weight, however, you'll see some of the same folks also using a bivy and thicker camp pad. Both of which add more weight to the complete shelter system than is saved by foregoing the BT floor. But they may have other reasons than only saving weight, like ventilation, bragging rights, etc.
Having said that, I think there are times when either approach is appropriate. In hard driving rain, it may not be possible to find the perfect site for a tarp & flat groundsheet set up, much less spend much time looking for one. In this case, a BT floor may be the best option.
And, yes they can trap water if your overhead cover fails. I had my GG TheOne fill with water during a storm on the CT last year. Not a good thing to be bailing water while perched on a Z-Lite and trying to keep a down quilt dry, trust me!
So my recommendation is to critically assess your needs and make the right decision for your situation within your own constraints like cost. If you can afford it, the easy thing to do would be to have both and simply use what you need for the trip you're doing.