Why doesn't the block time influence time the amount of time needed for a transaction to be confirmed? Litecoin has faster blocks, but needs more confirms.

I understand this is because of possible reorgs, but how come it also needs 10 minutes for confirms even though the blocks are faster?
If a block is found super fast, like 1 minute, then you have your first confirmation in 1 minute. The 10 minutes is average of time between block confirmation. In fact, since the network in increasing in speed, we are more or less confirming block at 9 minutes each.

In some case, we are out of luck and a single block can take 30 minutes.

That said, the number of confirmation required to accept a payment is totally as the discretion of the merchant. You can accept with 0 confirmation, 1 or 2. Some go more than that but that should be for very big amount (like 100,000$ +).

Another alt coin can confirmed in 10 sec, that's irrelevant because 10 confirmations in that blockchain is still less secure than a single confirmation from the bitcoin network because finding a block in the bitcoin network is harder than finding 10 block in an alt-coin.