1. How do you account for multiple testing? To ensure that the treatment actually works, you need to show a statistically significant difference between control group and experimental group. If you start ten small studies, and expand them based on early results, you are likely to get more false positives (type I error).
2. In proper randomized trials, the statisticians, imaging analysts and sometimes even doctors doctors are blinded from the treatment and outcome until the study has ended. Blinding is especially important for earlier studies, where surrogate endpoints for survival are used (response to treatment in this study) to get quicker results. These measures can be subjective, and thus prone to bias if the studies are not properly blinded.
3. Earlier stage studies are used to estimate the treatment effect, upon which power calculations are based to determine the size of the study population in Phase III clinical trials. This strategy would bias the treatment effect towards a benefit of the drug (by selecting those studies that show a preferential effect).
4. Despite all these objections, note that the results presented are actually interim results of a study that intends to enroll 30 patients. Usually the speed of enrollment of patients is limited by logistics (Finding the right patients to include and getting informed consent from them) rather than the sequential nature of studies.
I recommend that you read the 'Statistical analysis' section of the published paper (freely available here: https://www.nejm.org/doi/10.1056/NEJMoa2201445), and think about how you would write that section with the method you proposed.