Immunoglobulin

No, no reason. IgA is the type of antibody present in secretions like tears
and intestinal juices. IgM is confined to the blood and particularly useful
for infection with pnemococcus and similar germs. IgG is the general type of
antibody used for everything else. You can only replace the IgG.

When intravenous immunoglobulins became available for therapy the companies making them were keen to market them. They were clearly of use in the rare congenital deficiencies of IgG, but they weren't going to make any money selling into this market. So they designed clinical trials where intravenous immunoglobulin was given to other causes of low serum immunoglobulins like CLL.

You can imagine that they were keen for these trials to succeed. However many of these trials showed no advantage until one trial eventually showed some benefit. But benefit was restricted to patients who had a serum IgG of < 3 g/L (or 300 mg/100 ml) and had more than one infection per year.

The IgG preparations do not contain any IgM or IgA so they are of no use for these deficiencies.

The real problem in CLL is the failure to produce an immune response against bacteria or viruses. This is particularly so for bacteria that have a polysaccharide coat like pneumococcus. This immune deficiency is made worse by treatment that hits the T-cells, particularly Fludarabine and Campath.