Yes, a lousy script isn't a fatal impediment. You can produce beautiful literature even with a poorly-designed script. And I suspect script complexity is only weakly correlated to literacy. Learning to read involves a lot more than recognizing characters and words. But a bad script definitely adds a layer of confusion that is completely unnecessary and ends up creating an elitist and cumbersome language.
The standard counterpoint to complaints about scripts is some form of whataboutism involving English. Yes, English is not remotely phonetic, but the modern form of the Roman script for English is actually pretty decent. It has a lot of visual differentiation between different letters. Compare this to Persian and Arabic where the placement of a dot or three makes all the difference between wildly different sounds.
The Roman script also has relatively few letters. This comes at the cost of ambiguity, and we need to make up sequences for certain sounds (th, sh, ch), but also means the learning curve is a lot less steep. Persian and Arabic have the huge mess involving initial, medial, final and standalone forms of a letter -- it serves no purpose really. Brahmi-based scripts are all abugidas which means vowels are folded into adjoining consonants and so you need to learn about 4X as many symbols as English.
You do have to guess what a letter sounds like in English (g,j,k,c). But this is also pretty common. Tamil doesn't distinguish between voiced and unvoiced consonants. This is an unnecessary annoyance. A much worse example is of Persian, Arabic and Urdu where the script allows one to drop a lot of vowels. This is especially bad for Urdu. For example, the Hindustani words for here (idhar) and there (udhar) are written identically in Urdu, so you need to "backtrack" to fill-in vowels appropriately based on the rest of the sentence.
Yes, English isn't phonetic, and is unstructured and unsystematic. But it is still a pretty decent script compared to some of the others out there. From an Indian perspective, I wish we could move to one script -- perhaps some variant of Devanagari for all our languages. There's really little purpose in differentiating between Gurmukhi and Devanagari. And we should just forget about Urdu all together. It made sense when the goal was to teach people one script that gave them access to both Hindustani and the official court languages of Persian/Arabic. But for today, Devanagari is vastly superior for writing any dialect of Hindustani. Similarly, Kannada has an almost bijective mapping to Devanagari, but each symbol in Kannada is just so much more elaborate and a pain to write. Life would be much better with one script.
Bring up changing scripts though and people -- and this appears to be a global phenomenon -- just go nuts! People need to realize that changing scripts isn't a terrible thing and has occurred many times for many languages. We're not going to forget our languages/culture just because we choose to change the symbols we use in writing.