> still adds up in a hurry

Never mind the wake word; a noise gate (which is a trivial computation locally in either hardware[1] or software) means we are not talking about [every second of every day]. I'm sure Amazon/whomever can do better than a simple noise gate, too.

Using GSM-HR which records voice at 5.6 kbit/s (a bit over 700 bytes/s).

    5.6 * 60 * 60 / 1024 / 8 = 2.4609375 MB/hr

Assuming a gate that only records 1% of the time, this is

    2.4609375 * 0.01 =   0.024609375 MB/hr
                     =  25.2 kB/hr
                     = 604.8 kB/day

    604.8 * 365.25 / 1024 = 215.72578125 MB/year

Assuming 40M devices[2], storing all the voice said around these devices for a year is only ~8 PB (8229.28 TB). Renting the necessary storage from Amazon AWS, from a brief look at their current prices[3] costs at most $200,000/month ("standard storage").

Yes, the storage costs add up over time, but the amount of data needed to record all the voice said around every Alexa in the world is trivially within Amazon's storage capability.

[1] voice activated tape recorders have been around for decades

[2] https://techcrunch.com/2018/01/12/39-million-americans-now-o...

[3] https://aws.amazon.com/s3/pricing/