I think it is important to differentiate between (1) musical accelerandi, ritardandi, and actual tempo changes, and (2) the tempo variations people have recently started doing in mockups where they vary the tempo every bar in a nearly random way to make it feel more "human".
The first can be clicked out or have clicks drop in and out to allow for a conductor to work the changes.
The second are a nightmare when put to a live ensemble and make a simple cue a painful, even disastrous experience to record. The reason is that the click varies in wholly unexpected ways that don't reflect how players push and pull the tempo naturally. It's like telling someone to walk in rhythm but then dictating to them exactly when each foot should hit the ground for every step with slightly random variations that they can't see coming. It's impossible for someone to match.
Plus, that's not the way musicians think of tempo. The tempo or click is steady and then music moves ahead or behind it. The tempo itself doesn't change, rather the music pushes and pulls around it.
If the click is going to be randomly varying all over the place, it's better to have no click at all. Streamers and punches are a great solution, but when that wasn't an option I've even had a screen at the podium so that I can follow the song position line in the ProTools edit window and conduct where the key downbeats land. It's not as nice as having a big streamer, but hey, if you have a big screen, your eyesight isn't too bad, and you know how to properly conduct musicians, it's much more natural than a wonky, random click.
The most important thing when working with live musicians is that variations in the click or tempo have to be musical, not simply frequent and random.