I'm not sure it's not allowed. I can make a bit of paper saying "I, Tim will pay the bearer on demand US$1 * the current CPI / 238" and sell it to you for a dollar.
Some reasons why inflation free currencies don't work very well in practice are if there is a lot of debt in society and the economy turns down it can be useful to inflate the debt away a bit. Otherwise you get Greece. If they were still on the Drachma with debts in that they could just print a bunch more and have the economy back to normal. Instead they owe Euros which have about zero inflation and are basically bankrupt.
It's not really about benefits to the government - they can grab what they want as taxes. It's about bailing out the over indebted. Sure you could let them go bust and let the banks that lent to them go bust etc. like they used to in the gold standard days but the majority of people don't want to go back to that.
Some reasons why inflation free currencies don't work very well in practice are if there is a lot of debt in society and the economy turns down it can be useful to inflate the debt away a bit. Otherwise you get Greece. If they were still on the Drachma with debts in that they could just print a bunch more and have the economy back to normal. Instead they owe Euros which have about zero inflation and are basically bankrupt.