Internal shutters and curtains absolutely do a lot. The difference is most noticeable here in the kitchen, simply because I am more likely to forget to close the blinds there, but it is several degrees cooler after a day of sun intercepted by the blinds versus sun pouring directly into the room. The difference comes from the fact that visible light is reflected straight back out of the window (rather than bouncing around inside the room, heating up each surface it hits), and that a layer of hot air develops behind the blind - this hot air passes its heat slowly into the room, yes - but it also conducts into the outside. Because the air directly next to the window is significantly hotter than it would be with no barrier, it conducts outside much faster than it would be (because rate of heat transfer increases with the difference in heat). Meanwhile the heat transfer into the room is slower (because it's instantaneous if you allow the sun in).

I hope we start putting external shutters on buildings faster. Everyone getting A/C is unsustainable, and as you say, it's a lot for just a few weeks each year.