Any change in subwoofer frequency response also results in phase reponse change. Group delay is a function of how quickly the phase is changing with respect to frequency.
Group delay will always noticeably increase with a bass reflex subwoofer at/near the system tuning frequency, since that is where there is an obvious and fairly abrupt change in FR (the shape of the knee/corner).
The use of a high pass filter to enhance woofer protection below system tuning will also affect phase response (and hence group delay) since it will typically sharpen the shape of the corner/knee and increase the slope of the roll-off.
If the F6 bandwith of the corner/knee is wide and gradual, GD will be lower. If the F6 bandwidth of the corner/knee is sharp/narrow, GD will be higher. This can easily be seen with GD plots of the PB13-Ultra in the 20 Hz mode vs. the sealed mode. The sealed mode is low Q with a very broad F6 bandwidth and a 2nd order roll-off. GD is accordingly lower than the 20 Hz tune, which has a much more sharply defined corner/knee.
Regardless, I wouldn't necessarily characterize GD as ideal/better/worse; it is merely a mathematical expression of how quickly phase is changing with respect to frequency, and can easily be predicted by simply looking at the corner/knee. And the shape of the corner/knee and the attendent roll-off slope is a reflection of the design goals for the subwoofer.
A 90 degree cliff below system tuning with a brick wall high pass is not necessarily desireable, nor is a 4th order roll-off which leaves the woofer more vulnerable to being overdriven. The more typical/common ground is somewhere between those two extremes - a critically damped or slightly overdamped knee/corner with a moderate high pass to enhance woofer protection. Once those design goals are established and implemented, the FR is defined, and (by mathematical association) so is phase response and GD.
To answer your other question, the sealed mode of the PB12-Plus is virtually identical to that of the PB13-Ultra - low Q, very wide/gentle 2nd order roll-off. It is suitable for small rooms which exhibit a lot of room gain fairly early in the pass band (say <35-40 Hz) and which would otherwise result in an obviously rising low-end response in the 20 Hz or 16 Hz tuning modes. In a smaller and tightly enclosed room, the sealed mode has the potential to exibit a flat response and usable output to near single digit frequencies.
Naturally the downside of the sealed mode is a reduction in maximum output capability at the deepest frequencies, as compared to the reflex modes (at least down to the system tuning frequency). In a larger room which doesn't show much room gain until the very deepest frequencies and which requires a higher deep bass output capability to achieve satisfactory playback levels for HT without compression or audible artifacts, the reflex modes are typically a better choice.
Will the sealed mode sound fast/snappy/tight? That is really a function of the in-room FR and any attendent modal peaks/nulls and the room decay times. But to the extent the sealed mode can/will avoid a rising low-end response in a smaller room, naturally that will tend to sound more balanced/natural.
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Ed Mullen