I don't know why you would need iron because steel is better and you could improve it twice as much with the steel smithing perk.
I think it makes perfect sense to improve your skill with iron : it's very common (can only be more common than steel) and cheap. Same with leather from all the pelts you gather on your travels, even if you specialize on heavy, since steel armours require leather too and it makes sense to use what you've got.
The only thing that wouldn't seem natural is to always make the same items (like bows or helmets) for the best ratio exp/materials. When I play a smith, I prefer to make complete sets of armours and weapons to sell. Real traders wouldn't want to buy the same stuff again and again.
If it's a role-playing question specifically, as in whether or not it's believable for him to grind for experience, think of it like this: in order to get better at anything, you need practice. But you're not going to waste your best materials on practice studies. You don't break out your best canvas and paints every time you want to sketch a figure, and neither do you use up all your good metal when you're only trying to learn how to shape a helmet's curve just-so.
If it's not a role-playing question-- sure, iron is cheap and easy to come by.
In the real world, craftsmen continue to make things they already know how to make, and what they learn is how to make the item more efficiently. You get really good at doing tasks that you've done many times. The item may not be any better, but the efficiency you learn then gets applied to the skills you haven't yet mastered.
So, yeah, repeatedly making things you already know how to make is valid in a roleplaying sense.
if I was a warrior and could smith my own armor you bet if I could smith steel, I would pick that over iron any day of the week. But why would I stop there? What else can I make? Smithing and warrior builds go hand in hand as far as I am concerned. Smith away