Actually, the large scale trials in England are only expensive because of the way they are organised. One of our teacher-led RCTs has 900 participants and has cost nothing more than teacher time. Also, the large trials in education are trying to standardise their protocols over six months with large samples. Teacher-led RCTs often model a laboratory approach with many being single lesson studies.
RCTs don’t have to be expensive but when run by a research team the costs mount up. When we conduct trials we will typically employ research assistants, postdoctoral researchers, pay for buy out of teacher time and teaching assistant time, assessment costs, materials costs etc.
The answer is statistical. To get a reasonable effect size will depend on how much variance there is in the sample. In educational research there is usually a very large variance in the sample because learners will be very different for a host of cognitive, social and personal history reasons. This means you will need large samples to see anything significant. Bear in mind that there are lots of different ways of measuring effect sizes, but this rule applies to all of them.