It is a fact that the axes/labels are getting smaller with increasing resolution. To proove it, I uploaded the original output image to an image hosting service:
This is an image with a size of 3543x2362 pixels.

When I press 100% in my image viewer ( here gwenview ) my screen is too small to show the plot at once, but - when scrolling - the labels perfectly match to the size of the labels in the plot widget. When I enter "fit to page" the labels are tiny - but this no surprise, when you scale the image heavily down.

Increasing the resolutions leads to larger images. You will have to scroll more, but the labels will keep their size in 100% - and of course the image will be scaled even more in "fit to screen" mode.

I just changed line 216 of the mainwindow.cpp from the bode example and entered 300 dpi instead of 85 dpi. It is clearly visible that the axes are so small that they are barely visible if the whole image displayed on screen. Is this the desired behaviour of the function?
You told the renderer, that you want an image with 300dpi for a size of 30*20 cm. On a device with such metrics (maybe a printer) you will see the labels displayed in a very similar size as on the plot on your screen.

Again: a scalable vector graphics format is what you are looking for - and this is what the new double based render engine of Qwt 6 is made for.

Uwe