In my opinion, yes. That said, it's an opinion, and there isn't exactly a negative to keeping it 100% public aside from user privacy.
The way I see it: transactions are kept open to the public as they are often referenced to and used for reporting scam cases - referencing someone's clan history like an open book provides no such use (aside from the point of a clan leader, but not as a moderator or someone filing an official report).
As a normal user I wouldn't want everyone knowing every single clan I've ever joined to and left. I'm sure there are others who may agree and others who may feel indifferent, but that's from the non-administrative standpoint of a user who likes his fair share of privacy from the general playerbase.
There is a way to have clan owners or leader have a "rank", much like SMods or HS people do, where having that rank allows them to see peoples clan history, but blocks the normal player from viewing it? I don't know if that's even possible.
Undoubtedly possible, but what you're not understanding is that there are users who do not want to give you that form of information because they want their privacy.
Also could be easily exploited with our new clan system: you can create clans for free. Anyone would then be able to register a clan for free, be a leader, and then access the information.
Not opposed to Clan Squad, Clan Managers and Administrators having unrestricted access to the list, but again, from the perspective of a user who wants anonymity from the general playerbase, having the option to hide that information is a must.
But since the Users are the ones that "need"/want this information it would be rather useless if only clan staff can see it.
I cant think of a instance in which cs needs to know in how many clans a player was last Month.
Again, it's entirely opt-in/opt-out as far as showing and hiding your clan history—similar to how show and hide your age on the forum.
For the people who want to hide their clan history, they'll be able to hide it. For the people who want to show their clan history or are indifferent, they'll be able to show it to the public.
That doesn't deter people from clan hopping then though, which was the intention behind the original suggestion.