Slower level rising is good, but to allow the players to experience more adventures, participate in more stories and get a handle on their character abilities before they gain new ones. Not to allow experience hunting to be a purpose for the PC's, that just encourages meta gaming IMO
I think you have the wrong picture. Experience hunting is a practical strategy. It could lend itself well to min/maxing, especially in 5th Edition where I enjoy planning out my level advancements for picking abilities and multi-classing. I will often think of what I want my character to be at 20th level when I play. I am starting a new ranger now, and I wonder if I want to take a few levels as a paladin of the ancients. As someone recently pointed out to me, being able to advance characters quickly lets you play more different characters you want to, and in turn have more diverse adventures and experiences with different combo's and builds. So faster level advancement, too, can provide for more adventures and more play of the game (which is a GOOD thing).
The term, grind, implies a little boredom there but you'd naturally be free to stop whenever you want. In a good sandbox, the PC's can go wherever they choose, and most importantly, in any order they choose. The DM reacts to what they do, and spends most of his time just as referee.
Going out for experience is first done to test your mettle and get the lay of the land. Second, and not so much anymore but very commonly in the past, it's done as a matter of survival. Just getting to 2nd level will make the difference between life and death for many characters. Some may enjoy going on an adventure right away, but without assurances from the DM that the encounters won't be too difficult, it's only common sense to be cautious and try to be prepared. Adventures know about experience. They talk to one another in the inn all the time, and they understand that whenever anyone is starting out they need to give priority to getting more experienced not only for their own survival, but so they can get better work or take on more awesome adventures. Campaigns often start in the inn, and suppose you walk in and see a party of confident, popular characters telling tales to the crowd. Can you go up to them and ask to join their group? Certainly. They'll size you up, and if they're nice they'll tell you to get some experience first. They might take you on as a retainer, though, which is also an opportunity to adventure and hopefully come back in one piece.
The encounter tables could be brutal, too, so experience hunting was also dangerous. If you knew you wanted to explore a dungeon, say with 2nd level monsters in it for a quest purpose, naturally it would be better to get to 2nd level yourselves first. Every potential adventure is still just as interesting, and experience hunting is over the long term is heroic work that only aids immersion and verisimilitude. You'd be protecting the community from dangerous monsters, thinning their populations, and staying aware of what's going on in the land so organized enemies have a hard time putting their plans in motion. You will meet travelers on the road, farmers bringing their harvest in, and also be able to back-up other adventurers and the patrols of the local authorities who also may be in danger.
It's not any sort of cheating or meta-gaming. When no more monsters are out there, the land is safe.