Minichromosome maintenance proteins (MCMs) are DNA-dependent ATPases that bind to replication origins and license them to support a single round of DNA replication. A large excess of MCM2-7 assembles on chromatin in G1 phase as pre-replication complexes (pre-RCs), of which only a fraction become the productive CDC45-MCM-GINS (CMG) helicases that are required for genome duplication1-4. It remains unclear why cells generate this surplus of MCMs, how they manage to sustain it across multiple generations, and why even a mild reduction in the MCM pool compromises the integrity of replicating genomes5,6. Here we show that, for daughter cells to sustain error-free DNA replication, their mother cells build up a nuclear pool of MCMs both by recycling chromatin-bound (parental) MCMs and by synthesizing new (nascent) MCMs. Although all MCMs can form pre-RCs, it is the parental pool that is inherently stable and preferentially matures into CMGs. By contrast, nascent MCM3-7 (but not MCM2) undergo rapid proteolysis in the cytoplasm, and their stabilization and nuclear translocation require interaction with minichromosome-maintenance complex-binding protein (MCMBP), a distant MCM paralogue7,8. By chaperoning nascent MCMs, MCMBP safeguards replicating genomes by increasing chromatin coverage with pre-RCs that do not participate on replication origins but adjust the pace of replisome movement to minimize errors during DNA replication. Consequently, although the paucity of pre-RCs in MCMBP-deficient cells does not alter DNA synthesis overall, it increases the speed and asymmetry of individual replisomes, which leads to DNA damage. The surplus of MCMs therefore increases the robustness of genome duplication by restraining the speed at which eukaryotic cells replicate their DNA. Alterations in physiological fork speed might thus explain why even a minor reduction in MCM levels destabilizes the genome and predisposes to increased incidence of tumour formation.