There is more than one reason to read "masters". One such reason is field-specific and can be phrased as "read the latest work right before a scientific revolution" (standard example is the large body of work by Cayley, Sylvester, GordonGordan, etc., in the pre-Hilbert classical invariant theory). Often such results are more powerful in very specific cases of interest.
Another practical reason to read "masters" is to avoid embarrassment. Lots of (mostly minor) results are not mentioned in later treatises, so a number of people rediscover these results because they are either too lazy to read, or simply assume that "masters" couldn't have possibly be so smart to figure out these results back then... When going through the references in writing this survey, I read all 80 pages of J.J. Sylvester, A constructive theory of partitions, arranged in three acts, an interact and an exodion, Amer. J. Math. 5 (1882), 251–330. As a result, I discovered that a number of recent results were already proved there, sometimes by leaders in the field (let me not name them here - see the survey).