Although there are only 6 tiers, you don't reap the benefit of a new tier all at once. Every tier, you can make four permanent XP purchases, each costing 4XP. Usually, these are: an increase to one of the three stats, to become trained in a new skill (or specialized in one you already know - skills only have two levels in this game), to increase the edge of one of your attributes or to increase your effort value (which says how much effort you can use in one action). Once you have done all four, your tier goes up and you get whatever tier bonus your type and focus give. There is some opportunity for customization here, such as letting the player exchange these default upgrading options for a type special ability. There are also special groups in the setting that might teach you special abilities, though you need to exchange your skill pick for the tier to get the ability (and to be part of them, obviously).
As the system is, allowing the players to keep getting new special abilities after the 6th tier, like the nano's esotieries, wouldn't really harm anything, I think. However, skills are a bit more dangerous the GM allows players to use skills that are already very wide and cover a lot of ground. It wouldn't be difficult in that case to eventually cover almost every roll with a skill. But, if you plan ahead, it is workable to let players keep picking skills too. What really might mess up game balance, though, is if people keep increasing edge and effort. There is no difficulty 11 in the system, and there isn't supposed to be one. So either the GM start letting players do things that defy the limits of physics, or the players will be regularly doing the almost impossible.
I don't think the problem here is so much that PCs are supposed to be used for one shots as much as that their progress is supposed to rely more on Numenera. You ever saw one of the many D20 games that tried to remove the dependence the system on magic items by giving a lot of special abilities that basically emulated the effect of the said items? Well, Numenera kind of tries the opposite approach.