And those constraints are for political reasons. The Four Freedoms are a political ideology about how software, developers, and users should morally interact, and the GPL exists as a legal tool to support this political ideology.
Edit: clarification - by "use" here, I'm including "bundle it into a black box of hardware and sell that hardware."
No, it does not. It places restrictions on redistribution, not on use. You can use it no matter who or what you are.
> If you make modification to the code and do not share those modifications, you are constrained from using the code you modified.
Incorrect. You can modify and use it to your hearts content. You are only required to share your modifications source if you distribute the modified software.
This is is only true if you consider distribution as part of "use". You're fully entitled to privately run modified GPL code, even as a server or whatevs if it's not AGPL.
You may think that’s an arbitrary line, that’s up to you, but a line it is.