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'.
Came here to say this.
Multiple skill checks where any one is a failure is the exact same thing as disadvantage, except you can keep arbitrarily adding checks past
merely 2. If you've hit 5 or more checks the chances of failure, even if only a natural 1 fails, is now 20+%.
This was fine in systems like NWN and other 2.x or 3.x DnD builds, because the chance of failure really could be 5% on each check if you were a specialist, so adding an arbitrary string of them just made failure possible again-and besides, one of the best roleplaying dice checks in recent memory, the NWN 2 trial, was structured in a way that you didn't
need to make all, or even
any checks to succeed-the number of successes just determined how well you succeeded, in conjunction with the number of sidequests you did.
In this game, where even the most optimal persuader has 50-50 odds on some of these checks, the chance of rolling at least one failure in 4 to 5 checks approaches 100%. However many of these checks are fake, and don't actually do anything-meaning that it's merely completely pointless.
Here's how you actually do this, as a DM, by-the-by.
First, do single checks when possible. Make them appropriately difficult-for instance, convincing the ogre to fight without pay is an absurd DC, as it should be. Failure doesen't trigger combat though, which is precisely how it should be in that instance.
Second, ideally do 3-4 checks only if the system is supposed to be difficult, or a gradient of success is possible. You're on trial? You can get anywhere from guilty kill 'em, guilty imprison 'em, innocent insufficient evidence, to "Wow, they
were framed, arrest the prosecutor!". You can then gate the different results behind a ratio of passes to failures, making incredible success only possible for specialists, but allowing mediocre characters to stumble through and potentially swerve to their strengths if it comes to that (trial by combat as a last ditch to avoid guilty).
Third, when doing multiple checks and there is only one outcome-an intentionally difficult skill challenge-make it so that the first checks don't decide the outcome, but do impose
momentum. DnD 5e has a simple way to do this, advantage and disadvantage. The first check is to determine if they second is at advantage, and if you fail the second the third and final is at disadvantage (and if you succeed both previous ones the third and final is at advantage). In this way the other checks matter because you can end up with advantage or disadvantage, it's less random than a single die roll, and you're not making it arbitrarily difficult by accident. It also feels more like a dramatic conversation, where the momentum is building up to a crucial point-detective procedurals come to mind ("Here's circumstance, here's evidence, and there's the slam dunk").
There are a few other ways to handle this, but that's the basic idea. Only add long strings if you have a gradient of success or are using a momentum building system.
