The elite templates grant all weapon and armor proficiencies, all class features, normal saving throw bonuses, and two skills, so the only things you effectively alter are base HP, number of healing surges, and how many powers you get from each class.
Healing surges aren't added with a template. The rest is true.
This may be funny to say considering that we are discussing things way beyond the orthodox 4e rules, but these areas that you mention right here are where significant powergaming might come into play. If you can buid a character with the same powers, same class abilities, but you have higher HP, then why not? There seems like there should be a tradeoff.
I like the idea of having three classes in 3.x, but I am unsure that I like it for 4e. Kinda sets you up to be a Mary Sue. The ability to multiclass only into your template class is kinda cool though. You don't open any more multiclass combinations than core, you lose some of the wonkiness of core multiclassing like only ranger base classes can go into ranger PPs, and it allows you to fine tune your degree of multiclassing a little.
If you were to toss out the extra HPs, the extra AP, and the save bonus you gain from the template class you could end up with the core 4e feel of a fighter/rogue is different than a rogue/fighter, and the power level would obviously be higher than core, but not as much as just templating a PC. This seems like it would be a very effective multiclass patch.
So if you restrict multiclassing to the template class, you get three levels of multiclassing.
The Single Class Specialist. This guy goes Base Class with a template in the same class as the Base Class. He ends up with extra powers in his class and is able to choose two of the class ability options, for example both as a Feylock and a Starlock. No point in getting the multiclass feats. Extra oomph for a single class character and makes them still viable as PCs in the face of all the multiclass options. You up the power level by one class ability option and an at-will, and encounter, a utility, and a daily power.
The Dipper. This guy goes Base Class with a different template than his Base Class. He gets some the skills, defenses, proficiencies, and class abilities of the template class, but only enough powers from the template to function. By not taking the multiclass feats, this character keeps his main focus on the base class while allowing him to step into the role of the template when needed. I think that this is mostly what people wanted in a multiclass system.
The True Multiclass. This character goes Base Class with a different template than his base class, then multiclasses into the themplate class. He can pretty much go even split on the powers, gets the benefits of both classes, but he has traded deeper specialization in either class for the flexibility of both. Not bad. Not sure how this will compare with the Dipper and the Specialist power wise. Most of the really broken combos only require a dip anyway, so this might be the weakest choice.
There I go again, sounding like a pundit and not providing much substance.