Your inclinations seem correct to me, but I find if very challenging to be definitive without seeing images.
There are use cases where branding adapts - off the top of my head Apple comes to mind. It's either just the name, the name and the apple, or just the apple. The apple icon can have gradients and a "shine" or be a flat singular color. For video, Apple just used the top of the apple icon, not even the entire icon. All this could also refer to MicroSoft and how they adapt their branding. Or FedEx, with its multiple color variations based upon service. (Granted these are well established brands which offers some freedom.)
Multiple variations are not automatically a bad thing... it's more about how different the variations are and what specific aspects are changing. If the core imagery is conveyed in relatively the same manner, there may be no harm in variations. The key to brand usage is consistency. If variations can be implemented but remain overall consistent with each other, there's no harm. (Again Apple, MicroSoft, and FedEx come to mind - wide variations, but consistent overall shapes.)
The possible technical, reproduction, issues regarding a blur seem irrelevant. The conceptual usage of a blur is what I would question. A blur, in itself, seems counterintuitive to a "logo". But again, without knowing the company or seeing imagery it's hard to be definitive. A "blur" for branding, to me, conveys a company with a lack of focus which is rarely a favorable impression. There's a reason one would find it difficult, if not impossible, to find a well-established company that uses any blur in their overall brand imagery.
I do grasp the concept of "here's blurry, here's how we are more focused." or "Here's the old burry way... our way is new and more focused." However, trying to convey that narrative merely dilutes the brand overall. "Storytelling" is not a viable path for branding, in my opinion. A brand should be directly about the company it represents - it's mission, philosophy, or service/product. A brand is not about how or why the company is better than others. Wouldn't every company everywhere state they are better than others? Such narrative platitudes are meaningless to potential customers/clients - therefore pointless. For me, there's no place for comparisons or narratives in branding. Narratives are for the sales materials not the branding. In short, branding shouldn't "tell a story", branding should "convey a mindset".
I can't imagine how a "blur" is conveyed for something like a single color product brand placement (like a pen or keychain). And if it's conveyed well at such a small size, my inclination would be to use that variation for all usage. I, personally, am not of a mind to make a brand more visually complicated for some specific usage merely because it's possible. If a variation works well for silkscreening two colors on a t-shirt, then that variation should be used everywhere, as opposed to making the brand imagery more complex or detailed merely for web usage. Just because something can be done, doesn't necessarily mean it must be done.
And be aware "small thin lines" may not hold up at small sizes, which may negate the reasoning for creating such a variation. All lines "at size" will need to be no smaller than 0.25pt in stroke weight to ensure they are retained for most processes.
Form v. Function. Branding actually has an imperative function. It is often too easy to get wrapped up in the form and lose sight of the necessary function.
What may be helpful is how different variations are reviewed. All proposed designs should be viewed in 1 color (or greyscale) and 1" at its longest dimension. And viewed at arms length or farther. Often merely doing this can immediately eliminate proposed designs. If a logo doesn't hold up when looking at it this way.... it's not going to do the job it needs to do, even if it is stunningly beautiful full size on a web site.