Historical performance of a gambling site's bankroll investments can tell a potential investor a large number of things.
Sure, but that doesn't either make it predictive.
If there are large swings in the bankroll performance, then this is a sign that the maximum bet is sufficiently large so that performance can be impacted by the bets of a small number of whales (in other words the maximum bet size is larger then it should be).
We already have very robust maths to be able to reason about this, which is infinitely better than looking at some historical charts. The maths actually comes to the opposite conclusion, btw. If you're not allowing bets that would significantly affect performance (to a huge degree) you're leaving money on the table (in both terms of EV and expected bankroll growth)
If bankroll performance is significantly larger then the house edge over long periods of time, then this may be an indication that the casino is (at least selectively) cheating their players. This can also be detected if the bankroll performance is significantly greater then expected over short periods of time if there is sufficient amounts of gambling volume.
Players can robustly check if they're getting cheated using the provably fair. If the casino is cheating players so much that it effects the profits they can just not show that in the public stats (which they likely would, to avoid sharing it with investors).
If bankroll performance is significantly lower then the house edge over long periods of time, then this may be an indication that the site owner is cheating it's investors by playing against the bankroll with knowledge of the serve seed. This would be very easy for the site owner to do, and would be very difficult to detect assuming the site owner does not go crazy with stealing a lot of money from a single account they are gambling with.
While I agree with this in theory, as Dooglus said a few posts above, BTC Just-Dice's (which had phenomenal volume) was less than a third of it's EV. So clearly "long enough period of time" is going to be so long as not really useful (if you waited on the sidelines for JD's profit to reach 1% of its wagered, you would've missed they HYIP-level returns it generated. And very likely still would be waiting, even if it was still operating =)
A large amount of variance may also be an indication that gambling volume is too small for the size of the bankroll.
Or, more likely, an indication that people are gambling =)
Exactly how much deviation from the EV is necessary to make the above conclusions, and over what periods of time are both unknown and are both up to the individual (potential) investor to decide.
However yes, historical data should absolutely influence your decision to invest in the bankroll or not because this data can assist in helping you conclude if a site is 100% "above board" or not.
I agree with you here, and think showing data is essential. I'm not against automatically generating fancy charts, I just don't think it's that important =)