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Resolved dust continuum and CO line ALMA imaging, and in some cases detection of H$α$ emission, hint that young massive planets are abundant at wide separations in protoplanetary discs. Here, we show how these observations can probe the runaway phase of planetary growth in the Core Accretion theory. Planets in this phase have the right range of masses to account for the predominantly moderate contrast gaps and rings seen in ALMA observations. However, we find that these planets gain mass and migrate inward very rapidly. As a result, the phase when they could produce gaps with properties similar to those observed is very short, i.e., $t_{\rm gap} \lesssim 0.1$~Myr, independently of the disc viscosity parameter. This would require many tens to hundreds of gas giant planets to be born per ALMA system, violating the available mass budget of solids in realistic discs. This also predicts preponderance of discs with very wide gaps or complete inner disc holes, which is not observed. We show that suppression of both planet accretion and migration by a factor of at least ten is a possible solution to these serious problems. Future population synthesis models of planet formation should aim to address both exoplanetary data of older discless planetary systems and ALMA discs with embedded planets in one framework.