There are a fractional number of days in a year. You can't have a year with an integral number of days (without varying the number of days in a year, i.e. leap years).
The proposal to abandon leap seconds is appealing but as short-sighted as two-digit years. You'll have to dynamically adjust times eventually because the rate of the earth's rotation changes. We can either do it right, incrementally, and programmers can manage to implement a standard that's been around for over forty years, or we can ignore it and pass the problem along. I suppose I can guess what will happen there.
Let's face it: decimal time was really only intended for people doing lots of math work involving time. If the argument for base 10 is that calculations and representations are "easier" than base 12 (mainly because all modern human civilizations use base 10), why not make the argument that base 2 should be used, since computers virtually think for us at this point?
The real reason our representation of time is still so fucked up is that it has to be used by all humans, and all humans don't want to deal with lots of digits, fractions, floating point, etc. Sexadecimal is just simpler, even if we do have to occasionally jump through some hoops to keep this piece of crap timekeeping system in order. One second every couple years? Converting to decimal just to deal with little problems like that seems like a completely unreasonable suggestion to most people.
I never could get around the 1/4 day problem, and still had to account for leap years with a sixth non-month day every four years. It was a fun thought experiment as a teenager interested in math and science though.
60 is probably best, tho.
edit: And I just realized I had a typo up there; I wrote "13 months" when I meant "12 months". D'oh.
Your idea has definitely never been tried or abolished. http://en.m.wikipedia.org/wiki/Decimal_time
imagine splitting time not exactly in seasons begin/end (what was the last time you synched your clocks with a solstice?). no leap seconds. no 28-31 months. no 365+-1 years. even daylight saving time benefits can be worked in the system if we don't sync 100% with the solar day but skew it just enough that you get the drift to align things on daylight saving benefits and still can tell the time by simply looking at the sun.
it's not hard. just nobody has the balls to even suggest this seriously out of math circles.