Note: I am currently playing on Master with a Destruction mage with no problems. I have been anolyzing the game since release so I take it slower than others. I didn't even spend any perks at all until I was in my early teens with this particular character (I was anolyzing build potentials/paths).
Some people think that Destruction has a problem because it doesn't have the same max damage amounts as other skills. That is false, though, aside from pure number-crunching. In game, it doesn't matter because all that matters is that you survive. It's pointless to worry about killing something with 1 extra HP or 1000 extra HPs of damage. Either way, you achieve the goal of survival.
By 'pure" class of any type, no player is going to level only one single skill, not even in one of the three general schools (i.e., Warrior/Combat, Mage/Magic, or Thief/Stealth).
Having said that, it's critical to understand the specific breakdown of skills within a school, particularly for magic. Basically, you have 6 skills in each school. In magic, Enchanting is a general skill (i.e., it is also useful for other schools, not only magic school). The game design requires enhancements from Enchanting to cast very high level spells. The game design tells you other tbings, too, such as lower level soul gems being not much use for actual enchanting, and that such items should be used for recharging weapons (including staves). You will use Enchanting in any magic-based build as it makes no sense at all to violate the game lore by avoiding it (and on Master, it would be difficult to do so). You don't need all Enchanting, of course, because only the middle branch really applies for a pure caster (although you might take the right branch if you use staves a lot).
Of the other 5 skills in magic, two are support, and three are primary offense. You do NOT need all three offensive skills, and it would probably be rather pointless to develop all of them, or even two of them (one exception: see below).
Note: Alchemy is no longer part of magic school, but rather is in stealth. Therefore, it is not a skill you need to level early on, not until you finish developing the primary skills for a pure mage, if at all.
Exception: you WILL level Conjuration simply because Beth made the very silly choice to include Soul Trap in Conjuration rather than Restoration where it actually belongs (logically, anyway... I have no idea what they were thinking, and never have understood why they refuse to put Soul Trap in Restoration for all TES games). However, using Soul Trap is not really using Conjuration in its offensive capacity (i.e., you are not conjuring daedra, undead, or weapons).
Now, to build a practical character, you would select a primary offensive ability and a support ability. Example: Destruction plus Alteration (probably the best combo) or Destruction plus Restoration (okay, but I think Alteration is superior to Restoration for a Destro mage). Or you could do Illusion plus one of the other two, or Conjuration plus one of them. Those are the foundation of a mage build.
Early perks go into Enchanting, of course. You can also throw a couple of points into Destruction just to get the damage up, but it can also wait if you like. Once you get Enchanting to about 50, you can flip flop and continue to develop both skills (i.e., perks into them). Yes, other skills will develop, but not by putting any perks into them, of course.
Alchemy is one option to switch to once you have developed the Destruction/Enchanting skills. You could also use other offensive magic (Illusion or Conjuration) and it might be worth it to put 2 or 3 perks into Restoration just to get magicka regen, although it really shouldn't be required. Obviously, you could also choose to develop Archery or One-Handed as a support if you want. It's up to you, but it's not primary. Whatever you choose, switch the stone blessing appropriately (e.g., Alchemy would mean you switch to Thief/Stealth stone for development).
Bottom Line: you will not have problems with doing enough damage to survive if you follow this approach. At least, I certainly do not have problems.
Addendum: People have complained about one or morre mechanics in every TES game. For example, people found Illusion to be way overpowered in Oblivion. I find it bewildering how people can come onto these forums and state that Destruction is underpowered (or even ruder terms such as unplayable) just because the skill requires varies styles to be feasible while making other styles unfeasible. This is true for any skill set and any style (i.e., not all styles are compatible with all skill sets). I could not play a warrior type of character, for example, because I really do not do well with melee combat (at all). Likewise, Enchanting is MEANT to be used with Destruction. This is obvious when reviewing the way magicka works in Skyrim (i.e., anything that would be cast multiple times in quick succession would need Enchantment, as well as anything with very high - beyond maximum possible magicka - spell costs). Some people enjoy summoning daedra to fight. I find that boring and pointless, not to mention breaking my character concept (she is purely good, so would not be a conjurer, per se). Similarly, some people prefer upfront melee combat, but I cannot understand why (my characters don't like to get hurt).
Destruction is fine just like other damage-dealing skills, but like others, it has its own requirements to be effective at high level. K7Avenger and other posters who claim that continuing to level makes you weaker are incorrect, as I have explained. Such a view is correct if poor choices are made once Destruction/Enchantment are developed, but that's also true for any build. However, if you level by making choices that support a Destruction build, you will be fine. That's for most cases, of course. Even in a TES game such as Oblivion, there were cases where certain enemies had Reflect Spell and were extremely difficult for pure casters (i.e., you could easily kill yourself by accident).