So is your issue with specific events then? I'm pretty sure most major e-sports games have a mix of online and LAN play in terms of the various events that are held.
Not specific events, but rather online play of those events, whether it's the totality of the tournament or just the online qualification that leads to the LAN portion. Issues like the Starladder rescheduling and forfeiting are fairly easy to sort out with the appropriate rules and better match scheduling. Rule enforcement is also important via penalties and punishment, but unless it's a big tourney the big-name teams probably have more power than the tourney itself and thus rules can be hard to enforce.
Casters like to say how it's a small community, that everyone are friends, and thus implying that fair sportsmanship abounds, but money is at stake and we'd be fools to think that players aren't taking advantage and every legal, illegal, and unethical advantage they can.
Stream delays and ghosting - I've seen 6 minutes stated as a reasonable delay, but aren't most streams running 30s-120s delays? That's certainly enough time for useful intelligence on the current game.
Live spectator integrity - Are we to assume others don't have access to the live spectator stream to pass on real-time info?
Hacking and exploiting - We assume there isn't a map hack or similar.
3rd party interference - Fans trying to help their team and hurt the opposing team through griefing, hacking, DDoSing, etc. Would a Chinese team vs US team have no outside chicanery for their match? Or Ukrainian vs Russian?
Additional team members and outside tools - Presumably Dota2 doesn't output combat to a log that can be parsed in real-time, but an extra pair of eyes can track and confirm things like smokes remaining, Aegis time, Rosh respawn (random, but still) and big Ultis. There's no reason why software couldn't be running on a second screen that lists the status of such things, with a 6th man updating it as he listens to the team-speak.
General Internet lag, strat pauses masquerading as lag pauses, steam issues, etc. Didn't TL just lose a close bo3 final to EG where Fluff had to standin because Wayto couldn't connect for a game (or two)? Presumably TL preferred to have Wayto play since they would have had strat and practice sessions around that 5-man lineup. Isn't server selection usually done in a way to penalize your opponents?
Scheduling, rescheduling, forfeits, throws, early GGs, etc. What reasons should teams be allowed to reschedule and how can those reasons be verified? Would a team lie about a reason in order to gain more time to research their opponent or practice their strat? How about to ensure that their full 5-man can play (such as if one is ill)?
Online identity, standins, and ringers - Is it fair to bring in a standin at the last minute or should teams be required to register a standin at tourney start so the opponents can watch vods, learn his heroes and habits, etc. Would a top tier player use my Steam account if I paid him $1k to play for me in a competitive final?
Obviously, most of the above (and I'm sure there is more) goes away in a LAN environment, and teams that use the above during online play would be weaker during LAN play, but what about teams that wouldn't make to the LAN play without the above? That's incentive to cheat. Taking home $10k for first instead of $5k for second in some minor online tourney is incentive to cheat. What about a second or third tier team trying to make it to the next level (for sponsorship, publicity, tourney invites, etc)? Or a player trying to make his name on the scene?
Then there are also things like Adderall and other stimulants to consider that aren't exclusive to online play. Maybe these never get solved. I know I'll still watch and enjoy it, but as entertainment. Most likely they won't until something public happens in a big money tourney.
