Because dmarc, DKIM, and SPF validate the domain against the sending server, not the address.
When i send from noreply@ at work, it passes dmarc, DKIM, and SPF, because the recipient mail server validates the message came from an authorized mail server for the domain (mosty based on dns entries).
Without that validation, you can certainly still send emails, but most clearnet mail hosts will drop your messages. Google, Microsoft, and yahoo at the bare minimum will
No you can totally modify mail headers anytime you want to, just be prepared to get mail rejection if you're not following current mail security best practices.
I'd recommend just renting a cheap vps from vultr or something, then you can setup your mailserver to send from anything you like. That's how my mailserver works. I pay like $3 a month, and its plenty of space for a single user mailserver (i have like 3 mailboxes)
I did go through the work to setup dkim/dmarc/spf. Took a weekend, but wasnt too bad. My mail is received by gmail yahoo and Microsoft. I imagine doing the same with onion addressing would be complicated.