Its a question that gets asked all the time; however, charts are invaluable to traders (notice I did not say investors). They provide possible entry points and exit points.
Put simply if you looked at a chart and wanted to place a trade at say $40 but previously the chart had shown a reversal at that point would you still enter or would you wait until that level had been broken? I know what I would do and thats wait for it to break that level and then using what ever Technical analysis tools are available, and I like to use, I would look for confirmation. I would then look to see where the next potential reversal level is, if the possible gain is more than my risk (where I set my stop loss) then yes I would enter. Dont forget that to make money in trading you only have to be right more than 50% of the time and make sure that you dont risk more than you could gain. I think that somewhere on the course it was mentioned that Warren Buffet is only right 64% of the time. Money management and controlling your emotions is key to successful 'trading'.
Now investors that are prepared to hold for a long time might not be bothered about that level of $40 but then again if he looks at the same chart and sees that it had bounced a few times at this level, he may decide to wait to see if he can get it cheaper, why not? In the great scheme of things it may not affect him, but try and pass a $10 note on the footpath without picking it up - its called human greed.
When I look at the chart for CVN it is to see how its doing and nothing else as I am not 'trading it' I am 'investing' in it for what I would call 'long term', based on the available fundamental analysis (news), but if I look at forex I will be trading it and not investing in it, so therefore charts are invaluable as I cant be arsed to get into all the fundamental stuff (far to much) that could affect the currency pair in a day never mind a week, month or year. What I want from forex is quick in and out in just a few hours and key levels are essential.
I think, with what I have seen on HC ( not been on here long) is a lot of people think they are investors but in actual fact they are Traders and are looking for a quick buck and expect the price to just keep going up. That can never happen as it is a natural thing for people to take profits when they feel they need to and you will always get dips and spikes.
So in a long winded way of answering your question
it really is 'what ever rocks your boat baby', you either can understand them and like them or you dont fully understand them and dont trust them.
To use your analogy of the coin toss - using just a coin it could go anyway I agree, but put a small piece of gum on one side it could change the 50-50 outcome couldnt it? and if three toss's makes the coin fall gum side down, then its safe to say that this will possibly make the outcome more than 50-50 in coming events - thats the same as a trend line or support or resistance- one touch is just a touch, but three touches now thats more significant for traders on the smaller time frames and or investors on the larger time frames - its trying to 'edge' the outcome in your favour by what has happened previously. If you are wrong thats where your money management comes in and you have to be prepared to lose if you are trader otherwise you will fail by letting the fear of losing take over. Sorry but I love talking about it.
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