I must be the only one who actually finds the repeated skill checks a good thing - keeping thinks unpredictable and beyond the control of a single lucky roll.
Rolling more dice makes the outcome less random, not more. If you were to roll 2d20, for instance, you would have a drastically higher chance of hitting the midrange (high teens low twenties) of the possible outcomes than you would of hitting an extreme (2 or 40). If you just roll a single d20, you are just as likely to roll a 1 as you are to roll a 10.
In the case of multiple skill checks in a row, it just arbitrarily increases your odds of failure. 'More likely to fail' is the exact opposite of 'more random'.