The theory was bitcoin would have low overhead as the only limit was machine time which should be cheap. However, an artificial transaction limit was created which creates artificial scarcity and thus high transaction fees.

In theory a miner wants to have the highest number of profitable transactions possible, but we ended up with collusion to drive up prices and thus miner proffits.

The 7 transaction per second limit of BTC is completely artificial. It stems in the max size of blocks being capped to 1 MB. This was introduced by Satoshi Nakamoto way back in 2010 as an easy way to keep spam from flooding the blockchain. Keep in mind that back then Bitcoin was basically worthless, so one could spam the network with millions of transactions at very low costs, rendering it unusable to everybody.

Satoshi introduced the 1 MB block size limit as a temporary measure meant to be easily lifted as transaction volume and Bitcoin price increased in the future [1]. However this didn't happen, Satoshi Nakamoto disappeared shortly after and his appointed successor, Gavin Andresen, was ousted from the project and his commit rights revoked in 2016.

A lot of people tried to raise the blocksize, and all of them failed because the developers who took over Bitcoin Core have always refused. Given that consensus failed to raised the block size the Bitcoin ABC implementation split from BTC to create Bitcoin Cash (BCH) on August 1st, 2017. Bitcoin Cash initially supported blocks of up to 8 MB, which was later raised to 32 MB. Mainnet stress tests have proven that the network works fine with blocks of up to 20 MB, making clear that the 1 MB limit of BTC is as artificial as it sounds like. Because of the higher block size accommodating to more transactions the fees in BCH are consistently under 1 cent ($0.01), and the roadmap [2] includes features to keep fees low even as BCH price increases (fractional satoshis).

I highly recommend this article [3] as the most comprehensive summary of the Bitcoin scaling debate.

So the final question would be: is 32 MB blocks the best we can do? And the answer is a clear NO. There is much room for improvement and the limits are definitely much much higher. I recommend this talk by Amaury Séchet [4] and this article on Terabyte blocks by Johannes Vermorel [5] to learn more.

[1] https://bitcointalk.org/index.php?topic=1347.msg15366#msg153...

[2] https://www.bitcoincash.org/roadmap.html

[3] https://medium.com/hackernoon/the-great-bitcoin-scaling-deba...

[4] https://www.youtube.com/watch?v=Z0rplj8wSR4

[5] http://blog.vermorel.com/journal/2017/12/17/terabyte-blocks-...