I also found dealing with Bitcoin denominations to be both un-intuitive and tedious, even though I was math major and don't mind calculating, in general. I don't like having my thinking about money encumbered by blurs of how many 000000000000000s there are after the decimal point. Your suggestions do make sense, however, I have thought about this issue and would add my 2¢...

Some day Bitcoin may reach $1,000,000.00. It has been predicted. In this case, a satoshi would be worth $.01 or 1¢. This equivalence would be quite convenient and we would not have to overhaul the nomenclature back to it's original after an update. Furthermore, what about micropayments? If 1¢ (1 sataoshi) is the smallest denomination, there could not be anything less without a complete re-building of the system. Perhaps, we should really be thinking about having smaller increments of Bitcoin to anticipate future problems like micropayments.

Kudos to the boys at Ethereum who already anticipated this problem:

1 Ether = 1000000000000000000 Wei.
1 Ether = 1000000000000000 Kwei.
1 Ether = 1000000000000 Mwei.
1 Ether = 1000000000 Gwei.
1 Ether = 1000000 Szabo.