I think the right answer is if you don't want seed pods then cut the flowers off but leave the stem. That way the bulb can absorb the nutrients from the stem.

That's what I usually do unless you've got another scape about to bloom and you don't want it to look too messy. If your bulb is older and well rooted sometimes I just cut the stalks off anyway but if you've got a newer bulb with fewer roots then it's more important that what nutrients are in the stem be passed back to the bulb...Donna

Actually you should consider Photosynthesis from the scape and from the surface of the seed pods. These are all "tellingly" GREEN - aren't they?! *rhetorically asking*

On the other hand, the amount of "substance" being stored in them growing Seed Pods OVER TIME (a minimum duration of 6 weeks) is not "considerable".
On the basis of my Observation over Decades, the bulb is already being exhausted much earlier: During and from the rapid Formation of these Scapes themselves, respectively.
Particularly on freshly planted bulbs with poor roots.