You're not alone here. I've been fighting this issue for some time now, and can't get any pattern to it. I always start engines during pushback and then after setting parking brake and completing after start checks, I request taxi clearance. Sometimes MCE will allow it.. sometimes not. It seems to be a random bug. I would think they would simply remove the capability to deny taxi clearance. If I want to make that request at the wrong time, then so be it.
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Fleahead of Ohio