We have developed a statistical theory for columnar aggregates of semi-flexible polyelectrolytes. The applicability of previous, simplified theories was limited to polyelectrolytes with unrealistically high effective charge and, hence, with strongly suppressed thermal undulations. To avoid this problem, we utilized more consistent approximations for short-range image-charge forces and steric confinement, resulting in new predictions for polyelectrolytes with more practically important, lower effective linear charge densities. In the present paper, we focus on aggregates of wormlike chains with uniform surface charge density, although the same basic ideas may also be applied to structured polyelectrolytes. We find that undulations effectively extend the range of electrostatic interactions between polyelectrolytes upon decreasing aggregate density, in qualitative agreement with previous theories. However, in contrast to previous theories, we demonstrate that steric confinement provides the dominant rather than a negligible contribution at higher aggregate densities and significant quantitative corrections at lower densities, resulting in osmotic pressure isotherms that drastically differ from previous predictions.