Why do we think that the ridership would be 2 times to 3 times higher? When Eglinton West was originally planned as full subway, they were only estimating 4,100 pphpd.
It is reasonable to assume that ridership level in this corridor will be very dependent on the 1) length of the route, and 2) its speed. On one hand, Eglinton crosses the city in the middle, and intercepts nearly all major N-S routes. On the other hand, most of people who could use it, have alternatives (going to Bloor subway, or taking an E-W bus to Yonge or Spadina).
So, whether people choose to use Eglinton or an alternative route, depends on how fast Eglinton is, and how far it can take them.
For the original, short Eglinton West subway (5 stations only, Black Creek to Eglinton West, not even connecting to Yonge), 4,100 pphpd seems about right (perhaps even too much). Who would use that route? People living near along that part of Eglinton; people transferring from Eglinton West bus; and a portion of passengers from Bathurst, Dufferin, Keele, and Jane buses going downtown. And that's about it. For E-W crosstown trips, most would take Bloor subway.
If Eglinton LRT crosses the whole city but runs slower than subway, then again, many people will prefer to get to Bloor subway. In that case, the TTC projections of demand below 7,000 - 8,000 pphpd are probably valid.
However, if the Eglinton line (no matter subway or LRT) both crosses the whole city and runs as fast as subway (as they claim for the Don Mills - Pearson section now), then there is no reason for the demand on Eglinton to be substantially lower than the demand on Bloor. Bloor line does not have a lot of local density, and largely depends on feeder buses. And, south is not more dense than north. Passengers from feeder buses can transfer to Eglinton just as they can to Bloor. And in that case, the LRT capacity limitations might start to matter.