After years of experience doing short and long treks in various climates this is the first time I hear of a trekking umbrella. And honestly, I'm not convinced.
Yes, rain protection will be good, breathability is excellent and they are easy to set up and take down when the weather changes (even without taking of the backpack). The single big problem I see is:
Even the slightest wind will make carrying an umbrella, even hands-free, very annoying. Apart from the thing erratically pulling you here and there, or even breaking, wind will also very much lower the rain protection: if the rain falls with a slight angle you'll be almost sure to get wet at least up to your belly, not to talk of the arms which stick out anyway. So the umbrella will not be able to replace a solid rain jacket (which is important for other reasons anyway, like wind-chill).
So what are you essentially left with carrying an umbrella in windy weather? A very heavy and unwieldy hat. :P
If you are looking for additional rain protection beside your standard rain jacket I'd suggest looking into:
- a poncho/tippet: can be very comfortable as it feels a bit like standing inside a tent. Also I like to be able to just flap the whole thing back over my head (so it only covers my backpack) when the weather gets better, and be able to flap it back down once the rain starts again. Very useful in places like Scandinavia, Scotland or Alpine conditions, where the weather changes quickly and frequently.
- a decet hat: this is up to taste, but a rain hat will give you a lot more freedom (and breathability) than the hood of your rain jacket. And it will keep your glasses dry :)