It's not hard to see why the Orioles were interested in Davis, 27. They already have a very talented Davis of their own at first base, but Ike Davis would have provided the O's with a left-handed bat who could occasionally fill in at first and DH. Davis's best skill is his ability to hit right-handed pitching. He's a career .243/.335/.437 (.336 wOBA) hitter overall, which is fine, but against right-handed pitching, he has a batting line of .258/.358/.475 (.360 wOBA). He cannot hit lefties at all, however (.268 wOBA), and is about average defensively and on the basepaths. (His career UZR and DRS numbers are propped up by his rookie season in 2010.)
Other than the regular lefties in the lineup -- Nick Markakis, Chris Davis, and the switch-hitting Matt Wieters (who is better from the right side) -- the O's talent from the left side of the plate quickly dissipates. Ryan Flaherty and Steve Lombardozzi are much better with their gloves than their bats. The same can be said of David Lough. And Steve Clevenger is simply the backup catcher. In Norfolk, there's Henry Urrutia, but that's about it. The O's will have to look outside the organization if they want to significantly upgrade their left-handed bench bat situation.
Ike Davis would be a better fit on the O's than, say, Delmon Young, who is redundant on the active roster with the presence of Steve Pearce. But, as a minor league free agent, Young did not cost much to sign, and he's obviously expendable.
Regardless of the timeline of the O's pursuit of Ike Davis, they eventually signed a part-time designated hitter in Nelson Cruz in February. As long as Cruz is healthy, his name is going to be in the lineup, either at DH or in left or right field. Ike Davis would have been a useful bench bat, but it's hard to go overboard considering that he's useless against left-handed pitching and that the Orioles already have a full-time first baseman. If the price drops for Davis, the O's should remain interested -- which they might still be. But they were probably right in hanging onto Britton. Even though it's early in the season, the O's bullpen does look better with Britton in it. Maybe that will change in the next few weeks/months.