The question of whether it was a good idea or not IMO is mute point, your graphs only look at revenue and profit it completely ignores ATI's cash position which was in dire straits due DX10 debacle/2900 XT.
Also profits are misleading, in this sort of industry a lot of your expenses are R&D which is effectively salaries of people. Most normal business would just show these as an expense, ATI, AMD, Nvidia and Intel can claim that a lot of money they pay in salaries goes to product development that will yield future income so gets recorded as an asset on the balance sheet which inflates there profits somewhat. Actual net cash income from operations is much lower (i.e the actual cash you get in your bank after all your selling and payments to staff and suppliers).
For the consumer it was a good thing AMD came along and purchased ATI otherwise Nvidia would have had monopoly on the discrete video card market in 2006 rather then 2014. ATI needed AMD's collateral to secure funding and AMD need graphics IP for it's APU's so it was a perfect match (just bear in mind ATI wasn't AMD's first choice, it did try to buyout Nvidia before buying ATI).
Exactly this, people forget that AMD bought a failing company in ATI.