Can we just get three free dodges per day so I don't have to lose LP just to note have my time wasted for 30-50 minutes?
If everyone has a free dodge and decides to dodge 1 out of 10 ranked games, the first 10 ranked games you queued have a good chance of being dodged.
If the total queue times, bans, and the pick phase lasts 6 minutes before each dodge - you could easily waste an entire hour accomplishing nothing.
Not everyone that plays LoL can dedicate their entire day to the game - I'd wager the majority of LoL's player base only have 23 hours a day. And if a lot of players only have ~3 hours to play - you could frustrate a lot of them into not playing LoL after an hour, which would just make the perpetual dodge cycle worse - if people are willing to invest less time queuing for a game then it takes to actually get into games, there will always be someone with a free dodge, and they might just use it to get back at everyone else free-dodging their other 9 queues.
For everyone that does stick around - you obliterate any chance of communication in the pre-game if you make frequent dodges widely acceptable. Nobody's going to spend any effort trying to communicate if a good chunk of games will never start - which would be terrible, especially considering getting everyone on a team to their 1st or 2nd choice in lane positions usually requires a decent amount of communication.
Free Dodges is an atrocious idea that should never, ever, happen.