Random: I think you're just making an argument that maybe head-hitting finishes need to be done away with, which is probably worth talking about in another topic.
Flori: The only reason people go by whole seconds is for convenience, it doesn't make sense at all to check the exact times and then not go by them. Also, it would be much more logical go by a 1 second margin of error regardless of the truncated times, so that 105.5 and 106.5 would be considered a draw.
But if you're going to actually check the replay, the only thing that makes sense is going by exact times. If you're gonna stay in-game, the only way to make sure winners don't become losers is to say that 2v2 draws include equal times, and times with 1 second difference.
Also something to consider: ties may have a suspense factor, but they always favor the better player, and the larger the margin of error in times we consider draws, the more it favors them. Suppose you have an 82.5% chance of winning, and 17.5% chance of losing against a particular player. Then suppose a rule creates a 5% chance of a draw, and let's say the probabilities go to 80% chance of winning, 5% chance of drawing, and 15% chance of losing. In actuality, we might not subtract 2.5% from wins and losses evenly, but I think this works assuming both players have similarly shaped normal distributions of their times.
This 5% chance of drawing implies playing another game, so you could rephrase it as "5% chance of (80% chance of winning, 5% chance of drawing, and 15% chance of losing)". Or to just focus on the winning percentage, it becomes .8 + .05(.8 + .05(.8...)), which can be written .8 + (.05)*(.8) + (.05^2)*(.8) + (.05^3)*(.8) +.... This is just a geometric series, .8*(summation from n = 0 to infinity of) .05^n. You might remember learning at one point that a geometric series reduces to 1/(1-r), where r is the ratio. So this sum is equal to .8/(1-.05) = .8421, so the real winning ratio is 84.21%.
The effects are minor, sure, but worth noting. It's pretty much just the same reason that more rounds usually allows the better player to come out on top, although unlike say intermediate, switching who goes first each time doesn't have much effect in RR.