Dealer integrity notwithstanding, this is one of the main reasons why I have had significant reservations going EV. Everyone talks about the cost savings and all of that with these cars. However, if you are someone who plans on keeping these things indefinitely, you can begin to see the long term costs associated with them. Now this isn't to say that an ICE car cannot generate high repair costs either, so don't get me wrong. However, at least with an ICE car you can take it to pretty much any shop to get work done. How many independent shops are going to want to mess with an EV? Especially if they do not have the software, hardware, tools, and knowledge to work on them? In either case, eleven grand seems awfully high. I worked in a VW dealership briefly and I think the only time we ever gave someone an estimate that high was when they brought in an 80's era Cabrio that had been sitting in a field that the owner wanted "fixed up" for his daughter to drive.
Like others have already said, for that kind of money you can buy a relatively newer used one with money left over - at least where I am at anyway. There are always '13, '14, and '15 models for sale for around $10K. Again, the OP may represent an extreme case here, but I think it does highlight the potential long term costs of ownership for an EV. This is what I keep telling Tesla people - imagine what that's going to start costing years down the road once the warranty is up
I agree with everyone else though - I'd sell that car to someone for a few grand and pick up a newer one (assuming they wanted another Leaf).