There are free software fonts available. But why government uses involves a question of million rupees. Lohit font, Droid Fonts, Noto fonts are all free fonts. Meera font is also created for the same reason you are taking about.
While talking about GPL to fonts it is necessary to understand FE also. Read about it here.
If you are ready to design fonts, yes hats off to you. Start with it.
We have some people who can help with it. But remember it is time consuming also it includes much designing work,