Without starting a growers debate , both methods work. But growth does not stop because it is in a larger pot. That is not true , the seedling and final plant will have unrestrained room to make as large of a root system it can grow or as large root system a longer veg time will get to grow..... Think about a planting a seed outdoors , do you keep transplanting a tomato plant over and over ? In a large flower bed , do you uproot plants to transplant ? I don't . I have a stupid fern in a terra cotta pot going on 2 years in same pot , and is healthy as hell.
The main issue with large pot when you have a small plant / seedling is OVERWATERING. the larger size holds more water/moisture so you have to lower amount given to plant . One trick I have done is a prewetting of soil ( 24 hour ahead ) in large pot container before adding seedling , the moisture is enough to carry young plant for a good while . Make sure you have adequate draining whether from added perlite or other means.
By allowing the seed , seedling and final plant do its thing without unnecessary handling is the best for it. What benefit does it have on the plant to keep upsizing ? You can introduce stress and other issues. If you insist on solo cups , transplant into final pot. As the soil becomes SLIGHTLY depleted from initial growth , let the plant get its basic growth done ( then you can introduce 1/4 or 1/2 strength nutes ) .
Stop the madness of intermediate pot sizes.