The main point of using a pedal in piano playing is to sustain certain notes which fit together, and can't all be held down simultaneously. Mainly due to the span between them all. That's the case here, too.
The first arpeggio is a B♭ with an added 9th note - B♭add9. That chord works all the way through the first bar, and then there's another 'Ped' sign. It makes sense that in order to re-apply the pedal for the next bar, that first hold must be released in order for that to happen. So, in reality, there's no need to tell when that will happen - it's a given.
Press the damper pedal as the 1st note, 1st bar is played, and as the 1st note of the next bar is played, release and re-press. as the 2nd bar is a different arpeggio, which wouldn't sound good mixed with the previous.
Sometimes, as you suspect, it is necessary to indicate where/when the pedal gets changed - it's not always intuitive, but here, it's the only option that makes any sense.