You come to (imo) a key realisation at the end of your post "It's not really about emailing but about our relationship". That seems to hold the intent behind emailing: you want to be close to her, draw her to you, maybe remind her (by emails popping into her mailbox and basically you popping into her life in-between sessions) of your presence or existence (so she doesn't forget you? to keep you in mind when you're not physically there?).

Emailing makes you dependent whereas T wants to foster independence. She wants you to dig this strength (which is in you) so you learn self-reliance + to self-soothe.

What she says re being present is, she wants the feelings 'live' or raw. If you've already sent them, it's no longer as...powerful. And makes for less effective therapeutic work.

I think you should try it - for your sake. The good thing is, she is not imposing. She's letting you set the pace but the ultimate goal is for you to soar...to spread your wings and fly!

She really seems to want the best for you.