That's a result of your social contract with your DM. In my games, PCs start at 3rd level with 1,000 gp and no permanent magic items.
Look, if we're bringing "reasonable" in as a criteria, I'm going to win. It's not reasonable to change the ECL of a PC half way through a fight. The only hope for breaking Inspire Greatness was through strict rules application, as Hyp is attempting, but even that fails so far.
By the "reasonable" criteria, Inspire Greatness already addresses every major aspect of HD: it grants (an equivalent of) extra hit points, it grants an attack bonus, and it grants a bonus on saves. It even allows the PC to be treated as 2 levels higher for spells that care. Extra feats? Less XP? These things aren't mentioned in the text, and are frankly more trouble than they're worth.
You may have an intuitive grasp of what Hit Dice should mean, but IMHO you should pause and compare it with your intuitive grasp of how Bardic Music should work.
If you want to house rule that Inspire Greatness grants a bonus feat, do it. But do it as a house rule, on the basis that the bolded part here needs more beef: "A bard of 9th level or higher with 12 or more ranks in a Perform skill can use music or poetics to inspire greatness in himself or a single willing ally within 30 feet, granting him or her extra fighting capability." ... rather than on a misreading of the rules.
Cheers, -- N