In your third version you're saying the opposite of what you intended.
The idiomatic way is "Pienso que un estado grande no llega a la gente".
Your "be out of touch" becomes "can't reach" in Spanish. Gobierno is the group on people circumstantially in charge, May & Co. etcetera, estado is the set of public institutions that gobierno and all the public servants manage.
There's a lot of troubles with vocabulary there, and you choice in you user page saying "gender: I prefer not to say" makes it impossible to translate into Spanish. There's no way you can avoid your gender talking in Spanish.
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