Not GP, but if you are a person/business that has a lot of BTC, it's not hard to see the value here. When Dish Network added BTC payment as an option, it was really nice for me.
For someone who doesn't do the bitcoins, it was probably just clutter on the website. It's all perspective.
Exactly what is Bitcoin accomplishing in this scenario? Ohio won't actually accept them; rather, it contracts with a third party that immediately exchanges them for USD, which is what Ohio actually accepts. Ohio maintains no BTC inventory nor any exposure to Bitcoin. Not only that, but this apparently binds taxpayers to Bitpay's exchange rate.
What is this doing that you couldn't accomplish by simply selling BTC and remitting in cash?
That sounds suspiciously like the owner of the conversion service knew somebody within Ohio government's IT management, for values of "knew" ranging from "friends" to "bribed".
Value of tax liabilities and distribution of the debtors current holdings (BTC vs $) is a better metric to evaluate acceptable payment forms. Ohio state income tax rate is ~ 0.5% - 5%. Lots of 'businesses' don't owe anything. Accepting BTC may increase the likelihood of {high $ debtors who hold primarily BTC } actually voluntarily submitting payments. These 'businesses' would otherwise will be difficult and expensive try and to collect from.