Regardless, you have to admit that a Servant fight in a hospital could have ended a lot worse, especially with Rider busting out an A-Rank NP, even if nothing happened this time.
In this light, would you kindly wait until Sakura isn't in an area with that much potential for collateral damage before pursuing? Additionally, doesn't Rider usually go for a more subtle approach if one is available(Example: Fate route bad end at the temple, she specifically keeps Saber from reaching Shirou so she can't cancel the teleport that leads to Shirou getting his ass killed.)?
Rider was worried that Faust might hurt Sakura. She had to get to her to make sure she was safe. Plus, Rider didn't start the fight, Faust did. Rider had the option of either running away and leaving Sakura at the mercy of a potential madman or trying to grab Sakura and get her the hell out of there.
And, Rider couldn't care less about "collateral damage". Not when Sakura's life is at stake. Plus, in any case, Rider hasn't started a fight, or performed any sort of offensive action whatsoever. You really should be asking
Bdoom these questions, not me.
Rider also displayed capability of planning ahead to choose such battleground where she could take on Saber (until Excalibur got fired, that is).
Yes, but Rider didn't choose to fight this battle, and Sakura is potentially vulnerable. Rider was massively constrained by circumstances here.
And, she
knows fighting is a bad idea. That's why she intended to grab Sakura. She just didn't expect Faust to run straight for Sakura before she could get to her.