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Recent ALMA observations indicate that the majority of bright protoplanetary discs show signatures of young moderately massive planets. I show that this result is paradoxical. The planets should evolve away from their observed states by radial migration and gas accretion in about 1\% of the system age. These systems should then hatch tens of giant planets in their lifetime, and there should exist a very large population of bright planet-less discs; none of this is observationally supported. An alternative scenario, in which the population of bright ALMA discs is dominated by secondary discs recently rejuvenated by deposition of new gas, is proposed. The data are well explained if the gaseous mass of the discs is comparable to a Jovian planet mass, and they last a small fraction of a Million years. Self-disruptions of dusty gas giant protoplanets, previously predicted in the context of the Tidal Downsizing theory of planet formation, provide a suitable mechanism for such injections of new fuel, and yield disc and planet properties commensurate with ALMA observations. If this scenario is correct, then the secondary discs have gas-to-dust ratios considerably smaller than 100, and long look ALMA and NIR/optical observations of dimmer targets should uncover dusty, not yet disrupted, gas clumps with sizes of order an AU. Alternatively, secondary discs could originate from late external deposition of gas into the system, in which case we expect widespread signatures of warped outer discs that have not yet come into alignment with the planets.