I think there are (at least) two distinct questions in here, aren't there?
There's the issue of whether to be wide or deep in your selection of instruments to trade, and the matter of whether to be wide or deep in the selection in the types of trade you select.
I'm not convinced there's necessarily an "objective right answer" to either: both are going to vary according to people's objectives, aims and availability (hours), as well as according to their backgrounds and development of their trading skill-sets.
Still, in principle, I think "deep" is likely to be the right answer for most aspiring traders, most of the time, regarding the types of trading they aim for and the types of trade entries they seek to identify.
I suspect that regarding instruments to trade, it's less significant to be deep rather than wide, because there are more similarities and fewer dissimilarities, overall, between instruments (and even between instrument-types, given adequate liquidity) than there are between trade-types.
70% of my own trading is on one instrument (NQ), and the selection of the three others I routinely trade (CL, E6 and B6) was determined largely by my own background as a trader rather than (for example) by looking at dozens of different instruments and deliberately selecting them for any particular attributes (though these two possible methods of instrument-selection do actually overlap to some extent). You could call that "wide", in a sense ... or at least not "very narrow".
The types of trade I take are the same, for each instrument, and they're the type of trade that suits me and which in recent years I've studied and researched and practiced almost to the exclusion of everything else. You could certainly call that "deep".
I could switch to ES and A6 (for example) and trade profitably, most days, far more easily than I could switch to slower trading or trading with a different "style".
(I think Lawrence is right, in principle, to caution against picking up nickels and dimes in front of steamrollers ... but these things are all relative, and some people - including Tomorton, perhaps! - might even consider my own trading to be doing that. I'm a "semi-scalper", arguably ... by some people's standards, anyway ... though in my opinion the gap between scalping and what some people call semi-scalping is actually a much wider one than the gap between semi-scalping and much slower-moving, longer-term trading.)