A Bitcoin address is not necessarily a single-use token. Addresses can absolutely be reused. However, it's good practice to use a new address for each transaction, for reasons of privacy and security.
The privacy element was outlined in the Bitcoin whitepaper (section 10):
As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner.
The security benefit is that a Bitcoin address is a hash of a public key or a script, which means that if the elliptic curve cryptography used in Bitcoin is broken (allowing signatures to be generated for known public keys), we still have the hashing algorithms (SHA-256 and RIPEMD-160) helping to obscure the script or public key until a transaction is published. To spend the coins associated with an address, one must publish the original public key or script, but if you use a new address each time, the new address will have a corresponding public key or script that has not been pulished. Thus it would not be vulnerable to such attacks until you go to spend.
I would interpret the statement "A Bitcoin address is a single-use token." to say that a Bitcoin address may be used as a single-use token, and you should not assume that if someone once gave you an address, that will always be the address to pay to them. You should expect that there might be a different address each time.
Edit: Yes, reusing the same address provides a lot of convenience because you don't have to keep track of many different keypairs, and it makes things easier/cleaner if you can send your change back to the same address instead of a new one. (Edit: Note, as chytrik points out, good wallet software will handle key generation and storage for you, so this should not be an actual concern unless you are making your own transactions by hand, writing your own software, etc.) When you use a new address each time, you may accumulate lots of small amounts of bitcoin at different addresses that you can't recombine without associating those addresses. (Edit: I feel that this comment is worth reading and thinking about, BUT as chytrik pointed out, the privacy risk of reusing addresses is much worse than the risk from recombining UTXOs. I sort of intended this to say something like, "You're probably going to be losing some anonymity either way, so take that into consideration along with convenience when threat modeling and choosing a method." But I wasn't very clear about the level of risk in either situation.) It's definitely a convenience factor.
There are also obvious advantages to having a persistent address. It's much easier to use if you aren't specifically requesting payment from someone. For example, if you want to list an address on your website for people to donate to you, it wouldn't be very useful to have that address constantly changing. Some people also generate "vanity addresses" (see e.g., Vanitygen) which may have taken a lot of work to create, and they may not want that work to go to waste by switching to a new address.
