Should BTC have a first-seen-first-safe mechanism, for making fee lower?

Disclaimer: I am not encouraging any other currency and trying to adhere to the group rules as much as I can. This question is purely as a discussion of how Bitcoin can prove to be better than what it is today and that’s it.

I think that if BTC mining process follows a first-seen-first-safe transaction mechanism with 0-conf, the transaction fee and waiting times can be brought down significantly than what it is today. 0-conf alone is dangerous but think if your payment becomes irreversible then you need not rely on confirmation if you make a payment to a merchant and that payment will become instantaneous (which will be confirmed at a later point of time, but due to irreversibility, is a hundred percent reliable payment with negligible chances of double spending). Could you all see this as future of BTC? Your opinions are most welcomed :)