Dai, maybe, but Nazrin? This is pretty absurd. Unless you still have a few levels on your targets, Naz vs. Nature types is do-or-die.
Nazrin's not really so bad at taking on the early nature types. Daiyousei's stab attack is fairly weak and comes off her worse attack stat anyways, and she's got a good chance to just outspeed most Wriggles outside of Wriggle's Wriggle. The real spot she shines is just taking down all the early darks. Even if the earth typing holds her back some, Keine can just ride the backline until she gets strong enough to contribute too.
Human Village is probably one of the scarier parts of the game due to the low choices, but all of the Route 1 catches can really just take over even if you've picked a bad starter for the job. Nazrin/Shinmyoumaru both pull off the steel role well, Daiyousei can handle Cirnos easily, and Chen is generally strong and fast with nice early resists. The real scary thing that comes early is just Reimu, especially if she manages to get an attack boost off Metal Needle. The fact that most of those early catches level quickly can help springboard your team into a fairly easy cruise for a long time. Just catching all of those at the start of the first route ends up with a team that can outmatch Reimu's:
http://imgur.com/a/pAtDX#0I had a 10 level advantage on the Myouren Temple trainers. And I still didn't feel satisfied or even comfortable.
It's not actually rare for the speedy exp curve puppets to get far above other puppets fast. Trainers as a whole tend to be somewhat low outside of boss fights. The big drawback is that the fast exp puppets tend to be weaker and more gimmicky than the slow strong puppets. A 10 level advantage can really be cut down hard from that, seeing as you might not even have a stat advantage at all.
That's pretty obvious, but there's also the problem of the "new" puppets coming in underleveled and underpowered (e.g. in the Human Village, you have level 5-7 puppets for team 9 and their level 10-13 puppets). And unlike Pokemon, the grind targets aren't gonna be statistically inferior; they're gonna be even.
Seeing as everything on the team gains experience from a battle, it doesn't take very long for something to catch up to the rest of the team. If they're actually used in battle just once, they can gain extra experience from it too, which is a pretty strong change from needing to send something out on every pokemon like you'd normally need. Keine can really start contributing in Human Village right after just beating Cirno if she's decent enough to start, seeing as she gets one of the stronger early game attacks too.
Overall, once you get outside of earlygame's boss rush, everything just sort of slows down up until Remi decides to bully hard. It's really just those points, a couple of mountain fights, and then endgame that ends up being really spooky. Rather than grinding, just mixing a team up slightly can really help out if some members fall off hard, seeing as it's very easy to just get very ahead of most trainers. It's actually extremely possible to never need to touch a wild battle as long as you just explore areas well. Extra levels may not help as much as extra items, spell cards anyways, as the scary trainers tend to have good items and good movesets to make up for their lesser power.