Sure you do. You are confusing fur coats with investments. To how many companies in your 401k portfolio have you offered free consulting? With an investment, ownership matters. If you could spend $200k on a company for a 1% share or $100k for a 50% share of a similar company with similar prospects for growth, I would easily bet you would spend more time on the investment on which you could get the cheaper deal. More ownership means a greater return on your time investment.
It's more realistically the one where you spent $2mm for a 20% share or where you spent $500k for a 20% share. Most investors seem to target percentage ownership, not amount they're investing.
(I guess you could consider the case where you got one at a huge discount through luck -- getting a $100k product for $10k. Then, I'd basically treat it as a $100k asset for the purposes of how much to help -- the 10x gain on the $10k already happened the moment you made the deal, even if it's unrealized. I'd be happy to buy $100k negotiable assets for $10k, but in general, bargains aren't -- there is a reason you're getting a discount, ranging from the founders being noobs who will equally be likely to get taken advantage of by others later, or the deal has more risk than you thought, etc. There may be some cases where assets are systemically mispriced -- I think Dave McClure thinks non-US startups are one, especially from LatAm and SEA.)
If I were making an investment into a public company (or a really late stage private company, like investing in Facebook the year before the IPO), I wouldn't think I'd have as much to contribute, true, but I'd assume I could help a $2.5mm valuation startup about as much as a $10mm valuation startup.
(Actually, my #1 metric on helping would be "is it fun for me to help" -- I'd probably end up spending all my time helping portfolio companies with security or infrastructure issues, and would avoid helping with design, HR-fiasco, or fundraising issues. And, if I could get Apple, Tesla, etc. to value my advice, I'd almost work for them for free ($50k/yr?) just to make them 10x more secure than they are now. It's just easier to get someone to value your advice when he's paying you $300/hr.)
I don't dispute that some people would behave like you're saying, but I would not, and most of the professional investors (super angels/VCs) probably wouldn't. I think this might be the difference between "professional" investors and angels.