one thing in particular I see where using the second method would seem to be better is in mixing. If we use:


---alices signature---
coin abc
---bobs public key---
---alices signature---

it is technically possible for this to happen


---mixes signature---
coin abc
---Alices public key---
---alices signature---
coin abc
---mixes public key---
---alices signature---
---mixes signature---

sorry probably fucked that diagram up but my point is Alice can get the same coin she put into the mix out of the mix. If numbers are used like the other option:

---alices signature---
alice: 0 mix: 1
timestamp (to prevent replay attacks)
---alices signature---


---mixes signature---
mix: 0 alice: 1
timestamp (to prevent replay attacks)
---mixes signature---

Now even though alice put in one coin and got one coin out, it doesn't matter because a coin is a coin.

Hope I explain myself well. Thanks!