You say that except...there are small data points that will be held against these actors just like the familiar characters. Regardless of how brief there comes an expectation of this character to be exactly the same. Pike has managed because Mount has charmed people and there is a measure forgiveness. But, that grace is very thin, at least for me.
I actually think Anson Mount doesn't do a good job channeling Pike. His Pike is very, very different - lots of swagger, very warm, charming, almost Kirk-like - compared to the original very cold, introspective, somewhat sad Jeffrey Hunter.
It's just easy to overlook for me because I'm absolutely seduced by Mounts charm and frankly prefer him as a leading character. But a big part is that I'm not very emotionally connected to Hunters original performance.
For Uhura that will be different and more difficult. I absolutely love Nichelle Nicols performance. Zoe Saldana is a fine actress, but I had already difficulties. This new actors also seems nice. But I absolutely don't see Uhura in her. I would 100% prefer keeping the same actress but just giving her a new name.
I don't even want to imagine my problems seeing another Kirk on this show... I just don't think that's a good idea.
"Batman" is a legacy character that can be interpreted by many different actors. "Kirk" is a character that was at least 50% pure Shatner, brought alive in the first place by this very specific actor and his mannerisms. Recasting him is bound to fail like recasting "Magnum" or "McGuyver" with new faces.
There is no good solution for any actor - either they stay too far away from the original. Or they veer too close to parody.
What Chris Pine & Zachary Quinto did was nothing short of a miracle - and STILL irked many.