I don't have a good intuition about how costly this actually is in practice, if you only play with 10% of your portfolio.

tl;dr extremely little.

Here's some numbers I made up:

• Let the market's single common factor explain 90% of the variance of each stock.
• Let the remaining 10%s be idiosyncratic and independent.
• Let stocks have equal volatility (and let all risk be described by volatility).

Now compare a portfolio that's $100 of each of a hundred stocks with one that's $90 of each of a hundred plus $1k of another stock. (I'll model each stock as 0.75 times the market factor plus 0.25 a same-variance idiosyncratic factor.) Compared to a $10k single-stock portfolio...

• the equal-weighted portfolio has $\sigma$ like $\frac{\sqrt{(75\ast 100{)}^2+{25}^2\ast 100}}{\sqrt{{7500}^2+{2500}^2}}\approx 0.9492$
• the shot-caller's portfolio has $\sigma$ like $\frac{\sqrt{(81\ast 100+900{)}^2+{22.5}^2\ast 100+{250}^2}}{\sqrt{{7500}^2+{2500}^2}}=0.9496$

...for an increase in $\sigma$ of 4.5 basis points. So, pretty negligible.

Even if the market's single factor explains only half of the variance of each stock, the increased risk of the shot-caller's portfolio is just 40 basis points ($0.7135$ vs $0.7106$). In the extreme case where stocks are uncorrelated, the increased risk is +34.5%, though I think that that's unrealistically generous to the diversification strategy.

Since an increase in volatility-per-dollar of $x$ basis points means that you give up $x$ basis points of your expected returns, I'm going to say that this effect is negligible in the "10% of portfolio" setting.