I’ve always been fascinated by quotes which are ambiguous enough to be simultaneously wrong and right.

In this situation, the ambiguity comes from ‘government’ covering three ‘patches of ground’.

‘Method of running a place/country’. (Self)Organized versus chaotic.
‘System in place’ which is used in running a country.
A particular group of people who man, at any given moment, the above mentioned ‘system in place’.

Now, which of the three meanings was at the top of Reagan’s mind when he was uttering those ‘famous’ words?

All governments suffer a recurring problem: Power attracts pathological personalities. It is not that power corrupts but that it is magnetic to the corruptable(sic). Such people have a tendency to become drunk on violence, a condition to which they are quickly addicted.

Frank Herbert

The way I see it, government ‘as a manner of running things’ is a very powerful method. Which had served us rather well, on aggregate. Only it is not fail-proof. Or, more exactly, fool-proof.
Government as a ‘system in place’ is a work in progress. We’ve been improving it since we’ve invented government as an alternative to chaos. Only we need to be very careful. As a man made system it will always be far from perfect. It has not been perfect in the past and, no matter how much effort we’ll put into it, it will always remain perfectible.
Finally, government as ‘the team temporarily in charge’ ‘suffers’ mainly from being composed of humans. Hence both corruptible and attracted to power. Hence liable to do everything to maintain their positions.

‘Liable to do everything to remain in power’.
Which means that it’s our job to keep them on the straight and narrow.
We, The People, are the first to experience the consequences of their decisions. Hence we, all of us, are those who need to keep Government – ‘the team in charge’, on a short leash.
If they want to remain in power, they need to keep us ‘alive’.
They need to keep the system in shape. Working good enough for the vast majority, not for just a few of us. For a few of them, to be more precise.

Otherwise ‘government as a manner of keeping chaos at bay’ would have failed.