What you are proposing only works if you have a device that only receives replies. That is not always the case.
Think of it this way: the postal carrier arrives at your house at whatever schedule the post office decides. You don't have control over that. The only way to get your mail is to continuously check your mailbox to see if anything new has arrived. It only takes 3 minutes to check your mailbox. For the sake of this analogy assume if the carrier arrives the next day and finds something in your mailbox they return it to the sender.
Conversely sending mail is different. If you haven't written a letter or packed a box there is by your choice nothing to do. That situation can persist for days, weeks, months, or even years if you have nothing to send outbound. When you have something to send it takes you over an hour to drive to the post office, wait in line, mail the package, and return... but there are no consequences if you don't go to the post office other than delaying your outbound mail.
Yes sending a package is expensive but it doesn't happen often and you can decide to wait until multiple packages have piled up to be sent making your trip more efficient.
Conversely you're paying 3 minutes to check your mailbox every day whether anyone sent you mail or not. If you don't pay the 3 minute price critical mail may be lost forever.
If you send a package once per month that cost 60 minutes but checking the mail an average of 27 days per month costs 81 minutes. Receiving mail cost you more time overall despite each receive attempt being 20x cheaper than each send attempt.
If I was finding that I am spending too much energy checking my mail for a letter, I don't presume that it takes me more energy to check mail than it does for me to send it. Rather, I presume that I'm choosing to go check my mailbox too often. That is literally all I am saying here.
Your logic on why that is, is effectively my assertion on why someone would find that transmitting devices are easier on the battery. People build the device thinking "the message could come at any time, so we always have to check." Stop doing that, and you go easier on the battery.
That is all to say, yes? We appear to be in fairly solid agreement on why a receiving device uses more battery. Has nothing to do with one being more battery per byte sent/received. Has everything to do with whiffing on many more receives than you do on sends. And is in complete control of the person building/operating the device.
Think of it this way: the postal carrier arrives at your house at whatever schedule the post office decides. You don't have control over that. The only way to get your mail is to continuously check your mailbox to see if anything new has arrived. It only takes 3 minutes to check your mailbox. For the sake of this analogy assume if the carrier arrives the next day and finds something in your mailbox they return it to the sender.
Conversely sending mail is different. If you haven't written a letter or packed a box there is by your choice nothing to do. That situation can persist for days, weeks, months, or even years if you have nothing to send outbound. When you have something to send it takes you over an hour to drive to the post office, wait in line, mail the package, and return... but there are no consequences if you don't go to the post office other than delaying your outbound mail.
Yes sending a package is expensive but it doesn't happen often and you can decide to wait until multiple packages have piled up to be sent making your trip more efficient.
Conversely you're paying 3 minutes to check your mailbox every day whether anyone sent you mail or not. If you don't pay the 3 minute price critical mail may be lost forever.
If you send a package once per month that cost 60 minutes but checking the mail an average of 27 days per month costs 81 minutes. Receiving mail cost you more time overall despite each receive attempt being 20x cheaper than each send attempt.