If not, there is something fundamentally wrong with the algorithm.
there is nothing wrong with the "algorithm". but there are a lot of things lacking from your knowledge about it.
1. transaction speed does not get any faster than this. it takes a couple of seconds for the transaction to propagate throughout the whole bitcoin network which is a global network of nodes. it is less than 5 seconds.
2. confirmation speed as above posted mentioned is determined by the time between blocks. and that time is a somewhat fixed time. bitcoin is designed in a way to have 2016 blocks every 2 weeks which translates to 1 block every 10 minutes. this doesn't change with more or less miners. when the number of miners (or more accurately the hashing power) changes there is thing thing called "difficulty" that changes so that we get the same 2016 blocks every 2 weeks again.
3. whenever you pay a fee (minimum amount) in the past 9 years in 99% of the history you could have gotten your transaction mined in the next block which is 10 min on average. but in 1% of the history of bitcoin we had spam attacks which filled the memory pool with a lot of spam transactions and created a fee war which meant you had to pay a higher fee to get a high priority.
and you are confusing this short period which has been over for about 6 months with bitcoin being slow!
