Who collects Canada Banknotes with Consecutive Serial Numbers?
IMO:
I don't know of any paper money collectors who actively seeks consecutive serial numbers unless its an acquisition of a run of notes which the collector typically wishes to sell off a few of the tail end of the run, (or to sell off a few notes which may be inferior in grade to help pay for the purchase). It is much more common to see a dealer acquire runs of notes because they'll buy them at discount (and may even mark them up for the neophyte collector). Some runs of modified 54's will sell for a premium but again- its a pretty tough sell for most collectors (like pushing a common $1000). Most collectors I know demand a discount for consecutive notes, even if they're a change-over, insert or short prefix.
Today, its just too easy to get a run of inserts let alone regular issue. We used to see radars and their "shoulder" notes which have become about as popular as "gold leaf" centennial notes (unless they're remarkable solids or 2 digit radars).
Sometimes consecutive radars which aren't really consecutive numbers because they would match a pattern of:
1001001
1002001
1003001 -which jump in increments of 1000- are collected by the radar people. Also, we've seen a lot of new interest in repeaters (& special numbers) though once again, they could be as popular as a "birthday" note, which has a very "select" audience.
The exception to this general observation (of luke warm desire for a consecutive run of BOC notes) is when one talks of Devil's Face, 1937 or 1935 (very uncommon). There is the odd collector who may like consecutive asterisk replacements or test notes as these are seldom seen/offered (except for some of the more common prefixes such as *B/M)
Whenever we see the rarer notes presented in consecutive runs- then it naturally piques our interest. How many of us are actually wiling to pay a premium for rarer consecutive numbers is hard to say.