Why not speed up block mining? After reading Why is increasing block size in the Bitcoin network considered to decrease security?, I have a follow-up question about increasing block sizes:
why do we not reduce the difficulty of PoW?
If I understood correctly, this would speed up the mining of the blocks, so we could do more transactions for a still low cost and keep security, is that right ?
why not reduce the difficulty of PoW?

I'm going to assume you mean we decrease the block interval, so that blocks are found more often than the current 10 minute target. Manually altering the difficulty would indeed allow blocks to be found faster, but only until the difficulty adjustment resets it.
So really, to change the block interval, you'd need to change the difficulty adjustment algorithm, so that the target time interval is shorter.

If I understood correctly, this would speed up the mining of the blocks, so we could do more transactions for a still low cost and keep security, is that right ?

Bitcoin's proof-of-work allows miners to turn energy into security, so the amount of energy spent per time is equivalent to the amount of security attained per time.
So we could allow twice as many transactions per time, but assuming the amount of hashpower remains unchanged, we will still have the same amount of energy being spent per time to secure those transactions. This also means that at the moment of transaction confirmation, the &quot;security per transaction&quot; would be halved, since only half the time has passed. After two blocks, the transaction would have security equivalent to a single block's confirmation on the unaltered chain.
Related: this is why blockchains which claim to have 'faster finality than Bitcoin' are a farce: the Bitcoin network consumes more energy per time (and thus provides more security) than any other network. The number of blocks that have passed is meaningless as far as security is concerned, what really matters is the cost of rewriting those blocks. For example, rewriting 100 blocks of a low hashpower coin might be cheaper than 1 block on the Bitcoin network. So in this way the Bitcoin network's single block provides more security, more quickly.
So, why don't we do this, and lower the block interval?
With respect to the question you quoted, it is worth noting that halving the block time would be equivalent to doubling the block size, in terms of the computational, bandwidth, and storage (ignoring pruning) resources required. Doing so would put more strain on network nodes, as it would require more resources to run one. With an increase in required resources, we should expect that less nodes will exist, and that negatively impacts the degree of network decentralization. Having nodes remain as decentralized as possible is important for the bitcoin network, as the value proposition of the network largely depends on it.
As Pieter mentioned in the comments, another negative effect is increased block orphan rates. I'll copy the text from the link in Pieter's comment, which was written by Pieter, and is a great description of the issues with decreasing the block interval:

There are two issues that get worsened by this:

The shorter the inter-block interval is, the more advantage you're giving to an attacker. You see, blocks take time to propagate through the network to all miners, at the very least limited by the speed of light. Due to PoW resulting in a Poisson process for block generation time, there is a nontrivial chance for two blocks being found within a very short time of one another. If that period of time is so short that the first block has not had time to reach the miner producing the second, the second block will be a waste of power (both in terms of income and in security to the network). This wouldn't be a problem if it affected every miner equally, but it doesn't. More well-connected (geographically centralized) miners suffer less, as they're relatively closer to everyone. But most importantly, a 51% attacker does not suffer from this at all, as he only builds on top of his own blocks, and thus never needs to wait for propagation. For some numbers, at block interval 600s there is about a 0.83% chance that two blocks are produced within 5s of each other. With block interval 60s that goes up to around 8.0%. If block propagation takes 5s, that means giving a direct 8% cost reduction to a mining collusion attack.
Overall resource consumption for full nodes. If you have 10x more blocks of the same size, full nodes will need 10x more resources to verify history and maintain in sync (bandwidth, CPU, I/O, storage, ...).


In my opinion, considering these negative effects, the linear gains in scale achieved would not be worth the work and risks involved in pushing out a rule change like this.