Not necessarily. If you want to ensure privacy, you could limit the selection of UTXOs to a single address, and even go so far as to send change back to that same address. This wouldn't be as effective as combining the UTXOs from multiple addresses, but it would help. The key is to do everything that can be done when building a transaction to ensure that as many inputs as possible are consolidated into as few outputs as possible.  

I would agree if you have multiple utxo for a single address then it makes sense since there is no privacy loss. However sending the change back to the same address would damage privacy (Hive does this) as it is then obvious from looking at the transaction which output is change and which output is sending funds. 

 Also not everyone is concerned with their own privacy, and I'm not aware of any HD-wallet implementations that won't already combine inputs from multiple addresses within that wallet without user input.

For people who do not care for privacy then it would work fine. But adding it into the wallet as default behaviour would deter those who do care for privacy - and making it a customisable option just adds complexity for the users. Wallets do need to combine utxo at times to spend bitcoins which is how people can be tracked today, using the minimum set of utxo tries to reduce the risk. 

Additionally, large wallets that have lots of addresses owned by multiple users like exchanges, blockchain.info, and Coinbase can consolidate UTXOs very effectively when building transactions

That's true - I'm not sure how they would feel about it though. I imagine they probably are already to minimise key management.