Why is it a pipe dream? Eliminate socialist tax-and-redistribute schemes, and tax bills would fall sharply, boosting take-home pay and saving ability substantially. There are very few areas of the country where a decent little house can't be had for $125,000. In a lot of areas it's less, and in areas where it's significantly more pay scales are generally a lot higher too. A two-income couple living on one income should be able to save $125,000 in 5 years, if they make an effort. For lower wage-earners this will mean putting in overtime or a second part-time job, but that's easy to do when you don't have children to take care of.
First, the part in bold will never happen. Next, you expect 2 working people to pay $25,000 per year OVER what their other expenses are for a house when they are in their lowest earning years. Even if their housing was half of their income (which wouldn't qualify for a mortgage, I believe), you're talking a combined income of $50,000 per year for two people in their early 20's. The median income for ALL Americans is only $42,000.
This says nothing of paying back student loans, or furthering their education. I'm not saying this can NEVER be done. But it is unlikely.