How often do these large motors start? The only time I ever consider using a breaker as the controller is if it’s something that starts maybe one or twice per year for routine maintenance and runs almost continuously. Breakers are not designed as contactors, they have a much lower finite mechanical and electrical life and are a lot more expensive. Their design is for them to only open under load as PROTECTION when other systems can’t act fast enough. Using them as contactors can cause excessive wear and increases the risk that when REQIRED to act as a protective device, something fails.
As to how you start, Across-The-Line or Reduced Voltage, there are other considerations to investigate. Many utilities will REQUIRE reduced starting current for motors over some value of HP, varying from 15-100HP. If you have been getting away with starting 250HP motors ATL with the breakers, either your starting duty is so low that they don’t care, you are “grandfathered” into an older program, or they are penalizing you heavily and don’t want their revenue stream to slow down. If you are grandfathered, be aware that any change you do that requires permitting may trigger a release of that grandfather clause and you will be forced to reduce your starting current now anyway. If your starting duty is so low that they don’t care, you might fall into that category where starting with the breaker still makes sense. If you are contributing to the dividends of the utility stockholders, you may want to look into better ways to operate in general.
As a plug for soft starters, they are the only large motor starter I recommend any more, other technologies have no comparable tangible benefits in my opinion. Just be careful in what you chose; the ones that look like a bargain are in fact usually a risk. There are ways of making them cheaper by using SCRs in only 2 if the 3 phases and although that technically works, they can ruin your motor. Steer clear of those, you want one that uses 6 SCRs, no exceptions.