I'm involved in a sport, where timings are taken to the second, where even the hours are important (as in, in some cases we're talking about a range of <4 hours to >6 hours, although in all cases the times-of-day of arrival are a precursor which could be spread across two, three of four hours'-worth of time). For events whose nature means times spread across the one-hour boundary (and
rarely get anywhere near two hours) you can generally shortcut to saying "fifty-nine oh-five" for [0h]59m05s and "[one] two thirty-four" for 1h02m34s, with the hours being optional in this particular example (but only because an exception would be so
utterly exceptional that it'd be of special note), but you've got to start having a system when dealing with times like 1h00m05s, because "one oh, oh-five" can be ambiguous if the gaps, pauses and such are not properly conveyed to the other party.
Of course, nobody mistakes 20 seconds for .2 of a minute. Well, they
do, but that's when people complain that their average times have been worked out wrong, because they just typed it into a calculator without apparent awareness of its sexagesimal nature. Nobody who
matters makes that mistake... (Well, they shouldn't, and they generally get picked up on it fairly quickly.
)