Advice: Asking past professors to meet for coffee
Hi everyone! I'm currently working towards applying for my Master's, and I am hoping to speak to professors I've had previously, about 3-7 years ago, for letters of recommendation, research and/or work opportunities, etc. I don't expect them to remember me, but I'd like to send some cold emails re-introducing myself, hoping to meet for coffee, take some time to chat, hear about their careers, and develop more interpersonal relationships with people in academia.
For more context, 2 big reasons why I'd like to meet for a chat are 1) I did fairly average in some of the professor’s classes I’m looking to email but I'd still like to get to know them as some of them are widely celebrated in their field, and 2) I'm pretty open to what may come out of any conversation, even if it doesn't end up going anywhere, but ideally any opportunity that could come out of it (mentor/mentee, letter of recommendation, research opportunities, etc.) I'd be very open to.
Would this be something that professors would be open to doing or is this seen more of a time-waster if I don’t specify what I am looking for? Also, what would be the best approach for me to go about sending these opening emails?
Any advice would be truly appreciated :) thanks!