Certainly for business and first - booking early does not guarantee the lowest price.
For example I booked a MNL-YYZ itinerary for May two months ago and got D fare basis and a week ago I noticed that I fare basis had opened up which is almost $1,000 cheaper.
My strategy for business class is to book as soon as I know my dates - and check back closer to the departure date. The cancellation fee on a J ticket is $0 and for a D ticket US$50 - so if Internet (business class I) fares become available it is possible to book the cheaper fare and eat the cancellation fee.
I guess booking early does mitigate the risk of prices going up (e.g. Fuel surcharges) but these are usually flagged in advance.