simplifying expressions - Why don't 1. (0. + a) or (0. + 1. a) simplify?

I'm handling some mixed-numeric-analytic expressions, and I feel I'm missing some subtleties of how Mathematica handles simplification of such expressions.

In particular, I was initially puzzled by the fact that

0. + a

(with a undefined) will not simplify to a, but of course this forgets that 0. and 0 are not the same, and that if, say, one later on sets a=1 then 0+a will return an exact result but 0.+a will return a float.

However, if one takes this a bit further, to the expressions

0. + 1. a

and

1. (0. + a)

then they will still be returned intact. By the criterion above, simplifying them to 1. a and 0.+a would be functionally equivalent, so I feel I'm missing something. Does Plus[0.,expr] only simplify further if expr is a numeric expression? Does Mathematica decide not to delve into the depths of expr, potentially taking some overhead in complicated expressions, to save some complicated analysis? Or are the different expressions not actually equivalent?

Or am I just over-reading into this?