Actually, this question can also be phrased more generally: On what side do exterior blinds really make sense if privacy is not an issue at all, and therefore it's just a matter of protection from the sun?
Or should you install exterior blinds everywhere if you have already done so to the south and west? The south and west are also fixed for us in this regard – that is, with exterior Venetian blinds.
I would decide according to budget, use of space and appearance, less on thermal protection.
We have a 12 m2 corner room on the first floor as an office with south/east facing windows, both windows with exterior blinds because we didn't want blinds and didn't want to mix blinds and shades in the same room. We have some trees to the east and the sun is low in the morning.
I noticed that this summer I forgot to put that easternmost window on the automatic timer for heat protection, just now. There is no significant difference whether the window is shaded or not. Our front door, with its large window area, is also on the east side, and the hallway behind it gets almost no heat. The house is sturdy, with lots of storage inside.
We have roller blinds for the upstairs bathroom and bedroom on the east, and I wouldn't want to do without them.
Outside shading always helps, but if the windows aren't huge, you can do without them on the east.
The best solution for the south / west side: patio awnings with an awning over the entire front of the window, if possible. When the sun comes out, just extend the awning and be happy that you can leave all the blinds closed. View from above, no direct sunlight on the window panes, but still bright and flexible!
We have mixed ones.
North only roller shutters, but they are also only contiguous rooms. East 1 exterior blinds in the living room, 1 roller shutters in the bathroom. South External blinds in the common room, roller shutters in other rooms. West 1 exterior blinds in the office.
We have nothing outside on the north side. The only thing on the east side is on the first floor in the main bathroom, nothing else.
The other sides of the building, which usually have much more glass, are augmented with exterior shutters.
East: roller shutters (bedrooms, kitchen, etc.)
South: Venetian blinds (because the living space)
West: no windows.
And yes, that's just fine. The east side is completely dark, which is good for sleeping and blocking out the early morning sun, the south side blocks out the sun but lets in light, and the north side is just the bathroom, toilet anyway.
Inexpensive, effective shading, and sometimes very beautiful is the window shutter. It is not only available with a pivoting hinge, but also as a sliding element – even optional with an electric element. I think it's a great alternative to exterior blinds.