Pretty sure it doesn't :) Unless you want a million (okay, couple of dozens or maybe early three digits) email addresses pre-added that you can "select" from.
PS. You might want to check that feature out that I explicitly named on Thunderbird desktop.
PPS. General observation: any software (or service) by Apple isn't even close to, and by that I mean within thousands of miles of, competent third party alternatives (FOSS or otherwise) :P
I assume Thunderbird just lets you type whatever you want there, which I concede is nicer. But in a pinch Mail also does this.
Also, while open source alternatives are generally more flexible than what Apple offers, sometimes this is not the case. Believe me, I use both based on whichever one meets my needs :)
I cannot set a random outgoing From: address when sending an email in iOS. In many ways I understand applications not wanting this feature. Non-technical people will see it and wonder: What if I put in someone else's email address here?