I am glad you have seen some positive things in eM Client. You are right, you have to think differently. This is not some clone of Outlook or any other email client. There are some fresh new ideas here!
The problem with eM Client not closing properly, and having to do a database check on restart, has now been fixed and will be included in the next release. That will make many users happy.
Hardware affects eM Client because it is a database, and read/write speeds on the hard disk do make a difference. But you are right, the graphics card has very little to do with anything here. One way to increase performance without changing hardware is to disable conversations.
The idea with archiving is to both save space on your online account, and reduce syncing many older emails. Therefore the emails are moved to your local folders. If they were moved to an online folder, it would not have any affect on these issues. I have a problem with you suggesting excluding the Archive from backup. If the emails are important enough to keep, why would you not want to back them up? If they are not that important, delete them then the backup will not take as long. There are other options where you can archive online through your mail provider, and exclude those folders from showing in eM Client. That could help. Or you could save the emails outside of eM Client. There are other possibilities to explore.
If you are having difficulty with Rules, maybe I can help. I love Rules. The thing is that if you have already read a message, and then mark it is unread, you cannot expect the Rule to be applied. It is different to a filter. A Rule is only applied to a message as it arrives, unless you run the rule manually afterwards. Again, if you are having any other difficulties with Rules, start a new question and I will see if I can help.
Gary Stewart has not explained what his problems are with eM Client other than some vague terms. If he would like to give some details, I am sure that someone can either help, or confirm any limitation in eM Client and thus give closure. He has been using the software for some time, so there is some attraction for him despite problems he has. It is unfortunate that he feels eM Client has let him down, but if he is happy with Mail, then that is really all that matters. There are so many different email clients, each offering different features and implementations. If something else works better for you, then why stick with something that does not.