There are issues, yes. That doesn't mean it shouldn't be done, but there are things to watch out for.
In particular, it walks around some of the ways that 5e uses to balance itself. In the 5e core classes, you have noncasters, full casters, half casters, and warlocks as something of a special exception. The core of spellcasting is shared pretty directly between the various casting classes, to the point that caster levels can stack for spell slots and it works. By contrast, 3rd edition and 3/5 went kind of crazy with embracing of wildly varied magic systems, and the binder system was out towards the wacky side.
Vestige effects are different than other things. They were intended to be. That means that if you don't know the 5e design assumptions cold, you could break one or more of them very easily, without thinking you're doing anything all that significant. Just for an example off the top of my head, "bounded accuracy" and "always-on stackable debuff auras" aren't necessarily going to mix well.
Vestiges stack with each other in strange and not necessarily easily predictable ways. If you want to give your players a reasonably large library of vestiges to choose from, with interesting and flavorful effects, then it's going to be tricky to make sure that you aren't unintentionally handing them more power than you intend. Further, it can be surprisingly easy to produce a vestige that suddenly becomes class-defining. Low-level summons in particular are much more useful in 5e than they were in 3.x, and Binder had a fair chunk of summoning access.
Or, to put it another way, you can do this, and it might well be worth it, but both you and the player ought to be aware going in that this is a class that's going to require some additional help to keep balanced, and will probably require tweaks to keep from being too powerful or too weak, even more than is the case with most homebrew. Hey, vestiges are fickle, right? Play it right, and it could even add to the flavor of the class. One thing that might help with that - if you can whip up something reasonably decent for the class features, you should be able to manage the balancing purely through tweaking various vestiges.
Also, the structural design assumptions of 5e may not jump out at you immediately, but they're very different than those of 3.x, and they're pretty important. I don't personally know them well enough to teach them all to you, but if you don't know about things like Bounded Accuracy, you should try to learn them before you move on to trying to a homebrew on the complexity level of the binder.