Did someone found an alternative to this issue ?

Yes, just display the Bundles Product and not the individual products for cart.items and also order.items and subscription items, it can get very mess displaying all individual products (also for composite products!)

What Joey is saying!

This would be so awesome to be able to send cart mails when using product bundles!

Configure {{ cart.items }} to not display items in Abandoned Cart emails that are hidden from view in the cart (in the product settings for Product Bundles).

Update {{ cart.link }} to work with Bundled products.