It still seems impossible to correct for everything. Sure, you could correct for age as you describe, but I imagine that landline phone ownership correlates with political opinions in all sorts of other ways too.
Furthermore, how do you gather the data needed to correct the polling numbers without being able to accurately poll people in the first place? Seems like a complete chicken-and-egg problem.
"how do you gather the data needed to correct the polling numbers" -> you use the census. You need some info about the total population, you get it periodically and it doesn't change that much; you don't need to repeat it for every survey.
[1] Assuming that you're not measuring average age or measuring 'who is at home', but if you want to see, say, the average political opinion of total USA population, which tends to correlate with age.