The secular service has to have a clearly stated objective, that objective must be measurable, and that objective must also be something that relieves the burden of the State to care for people.

I do not believe this is true. Universities and museums rarely have measurable objectives, often don't even have clear objectives, and are usually 501c3. Lobbying and advocacy groups like the Sierra Club are 501c3, despite not relieving the state of a burden.

The secular service has to have a clearly stated objective, that objective must be measurable, and that objective must also be something that relieves the burden of the State to care for people. If all three conditions are met, that secular service can keep its tax exempt status.

Where are you getting this? Most 501(c)3 non-profits in the US wouldn't meet that standard.