Sticking with your mailman analogy: If a mailman can't deliver more than 2.7 letters per day (sustained rate), or 7 letters per day (going flat-out, on a good day), and 10 letters per day need to be delivered ...there will be a growing number of undelivered letters at the post office. No matter how much you decide to pay.
The price of sending a letter will go up, until a competing mail service emerges & your overpriced mail service goes bankrupt.
In a sense, it happened with email. Email was invented and suddenly people could communicate with virtual mails, that didn't even have the cost of paper, envelopes and stamps. A tremendous volume of communications started being done through emails, however the overpriced mail service didn't go bankrupt. Alt-services also developed, mainly for premium and higher-speed deliveries (courier) that took further load off.
But bitcoin is more than a service. It's also a store of value, like gold, due to it's limited nature. Even at 0.x TPS, even if all bitcoins were placed in a physical coin (21m physical coins) and sold as collectibles, being the "first digital, trustless, decentralized currency in human history", their price, as collectibles that would rival in significance of human progression the first ancient minted coins out of precious metals, could easily exceed 1000$ for their numismatic value alone.
People would be surprised to know that there are uncirculated nickels, cents or dollars, that cost hundreds or thousands - way more than a bitcoin costs, yet bitcoin, historically, is far larger in historical significance than an uncirculated coin of a century ago.
What I'm saying here, is that the price of BTC has a lot of speculative elements, inlcuding being the first, being scarce, being the primary means through which all altcoins are transacted to/from (BTC/altcoin pairs), being able to currently transact by itself something like 500k transactions per day, etc etc. It's not just its capacity to serve a lot of transactions - which is not exceedingly good at, that is important. And even if it becomes good at that, then, by necessity, it will lose a lot in many other areas that make bitcoin what it is.
Re. "kicking the can down the road": Sure, that's the essence of life, the universe, & everything. We're all gonna die, the universe too. This doesn't begin to imply that we shouldn't "kick the [death] can down the road" by sidestepping a careening truck.
People do not really appreciate right now what blockchain size costs. This lack of appreciation was bigger, the further back you go and it will be increasingly smaller as we go forwards. If there was a "futures" price for blockchain size utilization, the futures price would be quite high - given historical trends. Giving far more space for cheap is not what should be done. I'm in favor though for providing more space at premium or escalating prices - in order to both increase theoretical tx/s and prevent abuse.
