the fund's size should be compatible to the cap of the target company ( small-cap, mid-cap and large cap). So a lot of actively managed small-cap funds and mid-cap funds are relatively smaller.
I don;t have small cap right now. I do have mid-cap value, which is constantly beat Sp500 index. I am going to look into an idex fund in small and mid-cap soon.
You analysis about why the actively managed funds are behind index funds is correct. However, it also tells us that these professional managers are not doing much better than index. If that's the case, for average Joes, it may not worth of the time and effort to try to beat the index.
Nice to chat with you!