The way we implement this, you cannot report to a manager who is the same level as you. A sufficiently senior IC with an entry level manager gets transferred up the org chart upon promotion.
In my experience that leads to the organisation hiring more people at the upper ranks of the management track, and the end result is that management becomes the easier path to promotion and most of your senior staff are managers, not ICs.
If you have a team of engineers rangining from L3-L7 (on Square's scale), and you want to hire a new engineer you'll interview, and then decide on a level based on the person's skills & experience. Probably you knew up front that you were targeting a 4/5 or a 6/7, but generally, you don't go looking for a L7 IC, you look for an experienced engineer and then put them at the level that is appropriate.
But if that same team needs a manager then your policy is that they need to be a L8 or above (otherwise you'll need to do a big reshuffle to move all the L7 ICs out). So now you interview looking for a L8+ EM, and you hire the best person you can find, and you make them a L8. Maybe they're at the lower end of the L8 scale, and you know this role will be a stretch for them, but that's OK because it's good to stretch people into new roles and you think they'll step up.
But, you would have made a different decision when deciding what level to give an IC. My experience has been that for ICs, companies (rightly) err on the side of caution and if they think that the new hire is on the lower end of the scale they'll bring them in at the lower level, and let them prove themselves.
So if you're asking Is this engineer a N or (N+1)? you'll be more likely to bring them in at N. But for a manager, there are incentives to bring them in at N+1 so that they can maange the members of the team who are N.
And now your standards for an (N+1) IC are higher than your standards for (N+1) EM. And when it comes to promotion time, the new hires form part of the benchmark. And your existing Level-N EMs are performing just as well as your new N+1 EMs, so they're good candidates for promotion. But your existing Level-N ICs are really only performing at the same level as your new Level-N ICs, so things seem to be balanced.
I don't think there are any easy solutions to this problem. If you have a policy of ICs reporting to higher-leveled EMs then you create a system that makes it easier to be promoted on the management track. But if you have ICs reporting to a same-(or lower)-leveled manager, then you have a perception (and possibly an reality) that being a manager gives you more organisational power than the same level IC.