IMHO, what causes that shattering, as opposed to a weak set, are damaged proteins. Proteins are damaged by excess handling (agitation, homogenization), and/or heat. Also, the milk itself may not be best. Could be lower protein, like holstein, or come from a dairy feeding rations that push volume and numbers (silage with concentrates, etc).
TA will tell you little except the freshness. You'd need to test for PF %, MSNF, BF, etc.