I have asked myself this question numerous times, "Does Rebooting a Franchise always mean Rebooting the cast?" Truthfully I am somewhat torn on this issue. On one hand, a reboot may be in order due to a terrible story coupled with terrible actors. On the other hand, it may just be the story that's terrible and the actors are doing their best with what they are given. The problem with rebooting is that if they want to make something fresh and new, usually this means scrapping everything (actors included) and starting over. However, I believe that this is not always the best way to do it.
For example, I did not like Superman Returns, at all, but I did enjoy Brandon Routh as Superman/Clark Kent. Some may argue he was just doing his best Christopher Reeves impersonation, but due to what the director was trying to accomplish with that film I believe that this is exactly what was asked of him. I do believe that the next Superman should be a reboot, but keep Brandon Routh (I could do without Kate Bosworth who was terrible as Lois).

I can also understand the problems that the idea of a Reboot without a Recast may cause for the average movie goer (which I will refer to as AMG from here forward for brevity's sake). IMO this group does not include the Fanboys/girls, who take time out to go on CBM or other similar fansites to keep up on what is happening with the development of the films. We would be well informed that it is a reboot and their would be no confusion as to why some of the actors have been replaced and others not, and why the new film has absolutely nothing to do with the previous. We could accept that and enjoy the new film for what it is, but for the AMG they would view the new film as a sequel and not understand how it doesn't connect to the previous film. For this the film may suffer sales-wise no matter how good it is. I believe that this is the reason most studios equate a reboot with a recast as well.
Now there are exceptions I know. For example, for the info that we have thus far on the Deadpool movie it will be a reboot, but Ryan Reynolds will return to the role. I think this works as Deadpool is not as popular to the AMG as it is to us Fanboys/girls. So the studio may have figured that it is an okay risk for them to take (then again it's FOX so I may be giving them too much credit). Personally I'm glad they stuck with Ryan Reynolds in the role.
To be clear I want to stress that I am addressing Recasting for Rebooted films, not as is the case in sequels that recast (IM2 - Rhodey). THAT I find annoying, but understand the neccessity sometimes, because actors can be divas, studio execs can be penny pinchers or clueless, or the actors just plain suck and should be recast (though we aren't always so lucky....I'm looking at you Kirsten Dunst).
There are plenty of examples of CBMs that I believe should have the Reboot treatment, but I like all/some of the actors in the original version. Here's just a list of a few of my preferences of Movies that should be Rebooted, but the actors that should be kept for the reboot.
1. Superman Returns - Brandon Routh, Kevin Spacey
2. Fantastic Four - Chris Evans, Michael Chiklis
3. X-Men Franchise - Patrick Stewart, Hugh Jackman, Sir Ian McKellan
If you read this entire post without getting bored, Thanks. Basically my point is if I had it my way, a Reboot would not automatically equal a Recast. I do support partial Recast if necessary, but keep the actors that did justice to the roles they were given and allow them to the opportunity to further explore those characters. Don't throw the baby out with the bathwater!
So if you would indulge me, I would like to know your thoughts on the following:
1. Do you think Reboot should always equal complete Recast?
2. What movies would you want to see rebooted with all/partial cast returning to the reboot?
3. How many years should pass before a reboot is attempted?