Can someone explain why it "is fairly easy" to do this in Bitcoin"?
I hope you already read what all things you need to do as a workaround in other chains that use accounts.
How to create a new address in bitcoin core:
Doesn't Bitcoin also require UTXO Sweep when consolidating BTC from many addresses to one address?
UTXO - Unspent Transaction Output
That's why you have "Coins" and "Addresses" as different terms. You need to spend, Unspent Transaction Output when creating a bitcoin transaction from scratch. This is different for every transaction even if they were all done to same address. You can try using createrawtransaction for better understanding.
UTXO consolidation is only preferred if you have lot of small inputs. Small here depends on amounts normally used while sending BTC from that wallet. If I have 1000 UTXOs in my wallet with each 0.01-0.02 BTC and I normally send 0.01-0.02 BTC in one transaction, I may not consolidate anything and spend them separately when required.
If at any point any business has lot of very small inputs, they can be consolidated when mempool is clear with 1-5 sat/vByte without affecting business assuming if you are running a business with so many transactions, must have other UTXOs to spend.
Consolidation after coinjoin also kills privacy and few other cases so it's always up to an individual to decide how he wants to spend UTXOs. Coin control features in lot of bitcoin wallets provide users with the freedom to easily select UTXOs for a transaction.
I was under the impression that BTC does not allow multiple public addresses corresponding to a single private key?
You can read more public key, private key and address using below links:
What is the relationship between a Bitcoin Private Key / Public Key / Address?
HD wallets: https://learnmeabitcoin.com/technical/hd-wallets
Not related to tracking deposit but still relevant to understand basic differences:
Batching is easier and cheaper in bitcoin: https://ethereum.stackexchange.com/questions/71261/how-to-transfer-ether-from-one-account-to-multiple-account/
Tx count and fees of UTXO chains can't be compared with account based chains (Few websites exist trying to spread misinformation). Below link explains the reasons and lot of people use coinmetrics data: https://coinmetrics.io/on-data-and-certainty/
Bitcoin doesn't have failed transactions: Do we have failed transactions in bitcoin?