Clearly I'm biased - no way I'll be able to convince you follow-ups are awesome, given I'm trying to show off a tool making them easier :)

I suggest you talk to someone in a position where curating relationships is key - founders, growth, agents - and see what they have to say about follow-up emails!

I'd say the advantages are: Show gratitude, reduce the hurdle for the other person to ask questions/reach out via email in the future, summarize the most important points made, stay top of mind with the person...