Chaosmancer
Legend
I think one of the things overlooked by the paladin v. monk comparison going on here is the adventuring day. There are 6-8 encounters in an adventuring day and if combats average around 4 rounds(I've seen 3-5 being normal), then you're looing at 24-32 rounds of combat an adventuring day.
That 9th level paladin and his dozen smites is going to have 12-24 rounds of combat where he simply doesn't have a smite to give. If he uses them up early, that's several combats where he doesn't smite at all. Meanwhile the monk with a couple short rests can flurry every single round of every fight. He does less damage, but is the slow and stead turtle(less per round over more rounds), rather than the speedy rabbit(a lot of damage in a few rounds). Further, since the paladin is doing much more in a single punch, he's much more likely to simply waste his smite doing 28 damage to something with 9 hit points left, so his fewer smites could be wasted despite being used to deal damage.
That's not to say that I don't think that the monk needs more help to bring it up to par, but just that I don't think it's quite as far behind as some of the other folks here.
As I showed here https://www.enworld.org/threads/playtest-6-survey-is-open.698851/post-9077832 this is missing some fundamental points.
For example, Paladin smites are worth more. You need to flurry four times to have the same impact as a single 1st level divine smite. So, with the paladin being able to easily smite 10 times the Monk would need to Flurry 40 times to have a similar impact. With 32 rounds of combat MAX in your assumption, they don't even have enough rounds of combat to do so.
And this assumes 8 fights, which we know most tables DO NOT have. It doesn't matter how slow and steady you go, if the finish line occurs BEFORE you can catch up. And since your average of 4 rounds is taking us into 10 combats per day, that becomes unsustainable. And that is assuming every divine smite is a 1st level spell, when they are mostly stronger than that.
And as the levels increase, the paladin gets more spell slots. By 19th level, the paladin can smite 16 times, meaning the monk needs 64 rounds of combat, or 16 fights PER DAY to catch up. Which is absurdly unrealistic.