Cheaper? I don't see how. We're filling from the same CO2 cylinders, and my total hardware cost was less than that of a midrange SodaStream without the adapter you describe.
More convenient? Maybe, depending on environment and use.
But mine has advantages, too: More fizz, no counter space required, fewer fragile plastic parts, standard components that are easily serviced/replaced, and the ability to carbonate liquids other than water without worry of backspray gumming up a countertop machine's internal components. (Your unit's instructions probably tell you to use only water, for this reason.)
> you can leave the larger tank shut off and away from living areas so that a leak doesn't pose a hazard.
I close my cylinder's main valve when it's not in use, and the two additional valves downstream of it (at the regulator and ball lock fitting) also work, so I think a leak is very unlikely. Even if there was one, I would expect it to be noticed quickly or else too slow for the released CO2 to cause harm.