Yes, Bain is part of the problem. The problem is our low tax rates. Higher top marginal tax rates favor capital intensive firms, as they have ample deductible avenues to sink their gross profits into. "Capital lite" firms are finance, professional services, media stars as they don't really produce anything, and don't use much capital to produce what they do. So, the corollary is true that low taxes favor these firms, and high executive salaries. We used to have 70% top tax rate on income exceeding $200k, from Kennedy into Reagan.
Since Reagan cut top tax rates, and capital gains, it simply made it easier to liquidate capital (selling off factories, off-shoring, out-sourcing) which corp executives could profit on the spike in profits in the short run. In the case of higher rates it's harder to justify selling a plant when you get taxed on 40% of the profits, versus the 15% tax today. I suppose you can also see how low taxes increase flipping, and speculation, as capital gains discourages seeking profit this way.
But, that's not the only way cap. gains works, capital (physical infrastructure, equipment, machines, robotic fabrication) ages, and as it ages a firm gets to write off or depreciate that loss of value. That write off is depreciated at the cap gains rate, so a firm can get 40% of their value lost to aging as a tax credit, versus 15%. So, the higher the cap gains rate, the advantage goes to more capital intensive firms.
The same is true for small businessmen and entrepreneurs, they're hard to tax cause they have so many things they can invest in, or co-mingle. If I have a great year, I can buy a new "company" truck for me to drive, and my gross profits are reduced by that expense. Other deductible expenses are hiring, employee benefits, bonuses, training, R&D, upgrading tools, machinery, and equipment. The higher the nominal tax rate, the greater the incentive to divert gross profits into deductible avenues to reduce my net profits, which is the rate firms large and small pay taxes on.
Now, a backwater country, or Confederate state might need to lower taxes to attract business, but the US has the greatest consumer base on Earth. Higher tax rates won't cause firms to flee; to the contrary, it will cause firms to produce more here, to seek those capital expenditures to reduce their net profits. The cost of our labor, are discounted by the tax rate. (Just as when one "writes off" a meal, they sort of get a discount at the top nominal tax rate--so at 35% (the current top rate) you essentially get to keep that margin, just as at a higher rate, you get that discounted at that higher rate.
So, firms like Bain are part of the problem, but they're in many ways a symptom of low tax rates, which encourages the financial games they capital lite firms play, that has elevated the share of finance from 15% when Reagan took office, to become 40% of the economy today. These firms don't add a dime to GDP, as they don't make anything, they and lawyers, accountants, bankers, even corp execs, don't make anything, they hopefully make the economy function more efficiently. But, if we suppress their salaries, with a high top marginal rate, say 50-66% on income exceeding $1million/yr, they will presumably generate those same efficiencies, but for a smaller cost to the economy.
GE and GM were manufacturing powerhouses domestically, who saw fit to create generous pensions for their employees. High taxes did that. And, since Reagan, both firms have ended their pensions, shuttered much of their manufacturing, executive salaries have skyrocketed, and both firms are increasing financial firms as domestic producers. Finance is 40% of the economy, and as such a very real "tax" on the economy.