Sending takes a few minutes of computation on your wallet - but that's not such a big deal as it's comparable to the time it takes for block confirmations anyway.

The problem is verification of private transactions is very slow by cryptocoin standards, and verification is something that every full node and miner must do. Zcash would fail if private transactions were used in large numbers, as blocks would take too long to validate for mining to remain decentralized; Bitcoin transactions are a few orders of magnitude faster to validate, with a 4x more conservative block interval and 2x smaller blocksize, and the Bitcoin dev community has had to make heroic efforts to further optimize validation.

There are ways to significantly reduce the cost of zk proof verification by batching (that are compatible with the existing Zcash protocol without a fork).

Prove it first by actually implementing those ways and having them survive peer review; this is highly experimental crypto so it's not clear what's actually possible.

Again, I don't think it's very responsible to knowingly release design a protocol that in its current form would collapse if heavily used due to a lack of safety limits.