I'm fairly certain I would rather collect the emails even if it means less retention. Not for marketing purposes but for support purposes.
With MakePostSell [1] a customer may add products to their shopping cart and interact with a shop as if they are logged in, but at the point of sale / checkout, we ask them to verify their email.
Don't bother. If you collect email addresses, it's PII and someday you will have to account for that.
Instead, give them a searchable FAQ or a wiki and an email address to write to for support. Connect it to a ticket system that autoresponds with a ticket number.
(then you added your second paragraph while I was writing this.)
We're hoping to test an email password recovery option after the account is set up. It builds on the idea of getting more information after commitment.
With MakePostSell [1] a customer may add products to their shopping cart and interact with a shop as if they are logged in, but at the point of sale / checkout, we ask them to verify their email.
[1] https://www.makepostsell.com