The best reason for encouraging people to save even when young may be that it helps form habits they'll be glad of later, including the habit of not trying to live "without financial constraints" (because unfortunately those are always there and you don't gain anything by pretending otherwise).
Also, I think your calculation isn't the best one: you need to look at the age-28 gains from having saved $1000 per year for 10 years -- including the fact that the resulting money is there just as if you'd invested it afresh at age 28. It's not as if putting money into savings at age 28 is an alternative to doing it when younger: you can do both.
Hello I'm looking for the LW on investing advice. Any suggestions? Thanks.
EDIT:
Several commenters gave the standard advice of "buy index funds". If you bought into the Nikkei between 87 and 94 you would have made a loss or very little gains until now(30 years later). So I would appreciate some more in depth discussion regarding when is it good to invest into index funds? If you search in reddit/r/investing you will find more nuanced point of views.
http://finance.yahoo.com/echarts?s=%5EN225+Interactive#%7B%22range%22%3A%22max%22%2C%22scale%22%3A%22linear%22%7D
In general index funds will reflect the underlying economy, in the case of the US it was a growing economy for the most part of the 20th century, so the index fund would be good advice in that time period. I have a hard time believing that it is still good advice now, when the economy is retracting or stagnating.
TLDR: reddit/r/investing has more nuanced discussions.