I agree you should test out trading styles that involve several timeframes as the primary focus (for example long term position trading might focus on weekly & daily, swing trading might focus on 4hour, and scalping might focus primarily on 5min and lower)
I read a book recently (I think by Van Tharp) and he has some very good insights about the trading time/style you choose. Most likely, depending on your inner self, there is a timeframe/style that is a very good fit for you. The other styles may not be a good fit for you and no matter how much you try to force them, they may never feel right. The author suggested several weeks of trading each different style (ie position/swing/scalp) and see if any of them “speak to you” – you will probably know which one is best for you after doing this exercise.
Once you’ve identified the style of trading you will focus on, then I agree you should at least be AWARE of activity in the higher-up timeframes. However, this does not always mean you have to be looking at multiple timeframes throughout your trading session. For example I look at them once, draw trendlines (which are carried to my primary trading timeframe) and then I no longer need to look at anything but the chart I’m placing trades on.