I have now tried several cookie consent plugins on several websites and there is always once in a while a hiccup that happens where the site stops working once the pop up is displayed.
Today by pure luck I found an advanced setting under of the plugins that allows you to "Reloading the page on consent action" This has fixed the problems where in the minority of cases, functionality breaks and when I mean functionality, I mean things like the Mega Menu freezing completely or big issues.
So my question is, is this specific to the plugin or do all cookie plugins come with some degree of issues ?
What I don't understand, is why do these problems happen sometimes and not all the times ?
What is exactly happening here ?
Any help would be greatly appreciated.

We’d probably need a link to your website to figure out what’s going on.
What are you building the site with? Are you using a page builder, Gutenberg, ect.
Really, a cookie notice shouldn’t be breaking your website and it sounds like you’ve perhaps got a plugin conflict.
To answer your question directly – no, inherently cookie notice plugins don’t tend to come with any issues. I’ve built sites with Elementor and more recently using Gutenberg (with Spectra) and use CookieYes and in 30+ websites I’ve never had any issues.
If you wanted to debug, try disabling your other plugins and just having a cookie plugin installed. Then, one by one, enabled each of the other plugins and refresh your homepage before enabling the next one – probably in a private browser – to see when your site crashes. That way you’ll figure out what the plugin conflict is.