IE is expensive for a good reason, it's a scaling item. AD scales with crit and scales with AS, the more of each you have the more the AD is worth. If you have low AD then AS isn't worth as much, that's why the current builds for most Marksman is BT > LW, so that you have a good amount of AD for damage, you have some sustain and you have the ArP you need. Then you bring in the items that scale you into late game, if you don't buy the IE you don't have the scaling for late game.
And you don't build Botrk for the use on it as an AD, you build it for the HP damage that it offers per hit. If you are going an AS build then Botrk is miles above BT on damage, if you go BT you will need an IE, as the AD on it requires crit and AS for scaling, and the 250% crit damage from IE is huge at that point.
http://leagueoflegends.wikia.com/wiki/Infinity_Edge
Maths on the item their, the passive only needs to be worth 30g for the item to be cost effective. The passive is worth a lot more than 30g.