Even at the break-even inflation rate, isn't the YTM of a TIPS greater than that of a normal treasury bond?
Your analysis is incorrect.
The quoted market &quot;breakeven inflation&quot; is the spread between quoted yields. It is an approximation of the true economic breakeven from a total return perspective (possibly ignoring the par put on principal) to maturity, but under normal circumstances, it is not far off the economic breakeven. (Since the exact pattern of future CPI would matter, even the economic breakeven has technical calculation issues.)
Take an imaginary world with a 5% nominal par coupon, and a 3% inflation-linked par coupon (2% breakeven).

The conventional bond pays a 5% coupon.
The TIPS starts out with a 3% coupon, with the 3% of a par value that is expected to grow at 2% a year. It takes a long time for 3% to catch up to 5% at a 2% growth rate. (The principal future value increases by 2% per year, but that increase needs to be discounted by the nominal discount rate of 5%.)

The lower coupons are compensated by growth of the principal, keeping total returns equal.
(For an easier example, imagine a 2% nominal bond, and a 0% inflation-linked.)