It is possible to always have another block template available that does not depend on the transactions confirmed in the previous block. However, there are a few reasons why this is not done by default.

First, it would require miners to maintain a larger memory pool of unconfirmed transactions. This could be a significant overhead for miners with limited resources.

Second, it would increase the likelihood of creating blocks that are orphaned. An orphaned block is a block that is not connected to the longest chain of blocks and is therefore not valid. This can happen if two miners find blocks at roughly the same time and propagate them to the network. The second block to be found will be orphaned if the first block is accepted by the network first.

Third, it would make it more difficult for miners to coordinate their efforts. Miners typically work together in pools to share resources and increase their chances of finding blocks. If each miner is using a different block template, it can be difficult to ensure that they are all mining on the same block.

Despite these drawbacks, there are some cases where it may be beneficial to use a block template that does not depend on the transactions confirmed in the previous block. For example, if a miner is confident that they have a large number of unconfirmed transactions that will be included in the next block, they may choose to use a block template that includes these transactions. This could give them an advantage over other miners who are using a block template that does not include these transactions.

The decision of whether or not to use a block template that does not depend on the transactions confirmed in the previous block is a trade-off that each miner must make for themselves. There are both advantages and disadvantages to using such a block template, and the best choice will depend on the individual miner's circumstances.

In the specific case of mining pools, it is possible for them to create a block template that includes transactions that they have created themselves. This could give them an advantage over other miners who are not using such a block template. However, mining pools typically have access to a large number of unconfirmed transactions, and it would be difficult for them to ensure that all of these transactions are included in every block. Additionally, mining pools typically charge a fee for their services, and this fee would likely be higher if they were to use a block template that does not depend on the transactions confirmed in the previous block.

It is possible to always have another block template available that does not depend on the transactions confirmed in the previous block. However, there are a number of drawbacks to using such a block template, and it is not clear that it would be beneficial for most miners.