Of course I don't trust them, but they can stay as a member and never will be promoted. It's okay if they leave because they needed to find a better clan anyway.
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In my clan the reason why I don't promote members to elder or co-leader is because mistakes can occur while I'm away from the game. I do my job as a leader and I make sure that the clan is going well.
I really have trust issues...
As a leader, why don't you set some ground rules to ensure that your clanmates don't do the wrong thing like abuse their promotion powers?
On my Clash Royale team, I have laid down the rules that I only promote people to Co (my co-leaders handle most promotions to Elder) and also that absolutely no one is allowed to kick anyone unless they're causing trouble because I keep track of the activity data and know who is active and who will be kicked at the bi-weekly roster adjustment. Anyone that breaks these rules are either demoted or kicked, whichever comes first. My entire team respects that and my co-leaders help enforce the rules that I set. I trust that my Co-leaders will make smart sensible decisions when they promote players and they always do.
And if you're wondering what the overall atmosphere of my Royale team is like, it's doing extremely well and very positive. We are a constantly packed 50 player team, clan chat is always busy and everyone is motivated to play and contribute to the team events. I have 5 Co-leaders and a handful of Elders and Member-ranked players and everyone respects and follows the rules. Occasionally a newly-joined member might be unclear on the rules but the senior members are very helpful. Whenever they promote someone to Elder, they even remind the newly promoted player of our clan rules. I love my Clash Royale team, it's a awesome group of players. Originally, I personally appointed 6 co-leaders but 3 eventually left because they couldn't play the game anymore. And guess what, with the past two Co-leader promotions, I've given the entire team the privilege of voting for who they want as the next Co-leader (lol I bet that shocks you OP) and everyone that votes for the next Co-leader has placed thorough, well-thought out decisions on who should be a Co. In a way, the clan has become a close knit community of players and they don't want to see anything bad happen to the clan so their decisions are always in the best interest of the clan. I'm totally grateful for my awesome Royale team as well as my Boom Beach and Clash teams.
You'll need to trust your teammates more if you want your team to succeed. If you're going to put a tight leash on your team, your team will not be motivated to help you at all.
If you don't trust your clan mates then there is really only one solution. Create a ONE MAN clan as nullandvoid suggested below. You don't even have to create 49 more accounts; 9 more will allow you to do 10v10 wars. No good player will stay in a clan run with your style. So if you don't want people to constantly quit in the middle of wars or hop in and out you either need to change your management style (not likely given what you have posted) or just do a one man clan.