For inflation-linked bonds, that inflation expectations component does not exist. Instead of getting this inflation expectation component in the yield, you get the actual realized inflation. A regular bond is going to move its bond price based on changes in the real yield and based on changes in inflationary expectations. The inflation-linked bond will only change based on changes in the real yield. What happens is, inflation-linked bonds yield volatility is much, much lower than the yield volatility of nominal bonds.
Inflation indexed bonds do have a role to play in a portfolio.
Probably in place of some of their nominal bond holdings for many investors. The reason is inflation-linked bonds have an expected return that's very comparable to the expected return for nominal bonds, yet their price or total return variation has a fairly low correlation to the rest of the bond market and other asset classes. There does seem to be a role for the type of security in asset-allocation portfolios. I don't want to get into any specific personal fund investments, but I will say that all my investments are in Vanguard funds. Fannie Mae and Freddie Mac go out and buy mortgages that pull together home mortgages and invest in them themselves as an agency.