No to the Bamboo Spear? It's often considered to be too long for anything other than anti-cav, it's certainly not reliable in melee fights.
There's always the possibility to having differing degrees of bonus damage to horses, the bonuses don't all have to be the same.
Pikes and long spears are doing just fine in Strat last night's battle was a testament to that. What this means is, when used properly with a team, its a great weapon. When used on its own for soloing, its not. You shouldn't buff something because people refuse to use teamwork on battle. If this means they are essentially a Strat only weapon, I won't lose any sleep over it.
I think what you mean to say is that in strat random players (those not using a pike) are
generally able to achieve more against a single reared horse, than on battle. This shouldn't come as a surprise though, often on strat everyone is bunched together closely(this doesn't necessarily mean more teamwork) and there are usually enough pikemen on, to spread throughout the team so there's never one far away.
This isn't just your normal case of increased effectiveness as item count increases either (like with archery, throwing, cavalry, and somewhat crossbows). Unlike ranged or cav, only having a single pikeman for a full team, won't really grant you much (as an anti-cav weapon), even if the other team only has one cav player. 30+ players simply span too much ground for one pikeman to cover, due the cav's mobility. Furthermore, it's not as though the pikeman often(or even can) rear and kill a horse from full to dead all on its own, especially against any of the better horses. More damage vs horses won't really change too much to be honest, especially if it's true that as things stand now, the pikeman by himself is mostly useless.
I don't think this argument really holds up, especially considering the other arguments I could have made. After reading your post I had to take a step back to gather my thoughts as I felt there were so many things wrong with it (still, it's a seemingly logical thought, although obviously biased.)