I agree with those that say Inkscape, it's where I've designed all my logos. However, I've been tempted to try using FreeCAD to do it lately. I'm not sure if it can export as SVG, but the thought of have a proper parametric tool for designing logos sounds up my ally. I tend to try to treat Inkscape like one, by liberal use of construction lines, but at the end of the day, it really doesn't like being that precise.

Inkscape is good for making icons, assuming you want vector icons.

What's wrong with Krita and Inkscape? Be sure to always use vectors for icon designs, you can raster them afterwards.

Emblem from the GNOME Circle. It's very basic but it doesn't take any time to make an icon with it.

Inkscape 100%

I'm a non professional and have limited talent. But I designed a few logos here and there (and still do) and the best tool for that is Inkscape in my opinion. GIMP is not well suited for this task, as it lacks proper vector tools and format support. Inkscape has excellent and professional grade support with easy to use interface. Krita could be used to create logos as well, because it has vector tools and format support, but I feel like the user interface and utilities are not as good as Inkscape for this task.

Unless you are an expert in Krita, and don't want to learn or depend on new programs, then you could stay using it for creation of icons. GIMP could be used for icons too, if you just want to create raster format icons (as opposed to vector). In that case, GIMP could be well suited for this task too.

I never used any other program to make icons, so cannot tell you about alternatives. And I have no intention or need for it anyway, because to me Inkscape is the perfect tool for that task.

I like to write SVG by hand with a text editor and Firefox, but that's probably not for most people.
I mainly like it, because you're entering all the coordinates as numbers, which makes ratios more apparent and also easy to work with...

from https://alternativeto.net/

mtPaint is a painting program which Mark Tyler developed from scratch so he could easily create pixel art and manipulate digital photos.

JDraw is a pixel oriented graphics editor designed especially for small to medium-sized pictures used to decorate web pages. It is completely written in Java, simple to use and saves (animated) GIFs, ICOs and PNGs.