TLDR: Got a PhD offer at top choice, all details checked out, and I want to accept now (much earlier than the April 15th deadline).
A colleague (at the professor level) I mentioned this to said I should wait as it could look 'too earnest' accepting roughly 10 days after notification.
Is there any truth to this claim? I.e. does it 'look bad' (i.e. desperate) if I accept now? I'm just genuinely excited and am ready to lock it in.
Additional details (from comments):
This offer is a 'hard' offer such that it is from the department, many cc'd people, and is in writing
I have other 'hard' offers from other universities and have yet to hear back from a few more
Other relevant questions:
Thank you all SO much for your input. I went ahead and accepted the offer and got feedback saying they appreciated the rapid response and the PI was eager to arrange a talk for next steps. While this is likely the standard positive response, I have marked Buffy's answer as correct. The first two sentences made the most sense: 'Actually, it is simple courtesy to accept as soon as you know you will do so. This helps the institution deal with its obligations to you and others.' I then let the other universities know immediately after and I hope this helps their search process.