I'm aware of DNS over TCP (and why nobody uses it, partially because it depends on operating system fallbacks, heuristics, or complicated configuration), but on the other hand: every operating system supports secure DNS by now, why not use it? It solves two problems, the first being the amplification attack risk, the second being the risk of third parties reading, selling, and manipulating the contents of your DNS requests.
DNS over TCP is actually slower in many configurations, at least the ones I've tested. HTTP libraries and servers have been developed for fast opens with (probably protocol violating) workarounds for getting rid of the handshake in any way they can but DNS implementations seem to care very little, especially on the client side. 1-RTT TLS fixes serious connectivity annoyances while also providing security benefits at minimal overhead.
I personally prefer DoT over DoH, but the industry is moving away from DoT. Taking DNS, which is a fine protocol lacking encryption and sessions and adding encryption and settings is a very simple solution. An nginx stream proxy forwarding TLS traffic for port 853 to 53 is enough to set it up if you're not bothered by the handshake time that can be negligible in the age of 5G and fiber connections if you live in the right area.
Sadly, the "let's turn everything into JSON so I don't have to learn what bytes are" crowd won and becoming an old man yelling at the cloud doesn't solve anything. At least ODoH provides some additional benefits that just encrypting DNS doesn't at the cost of extra latency, though I'm disappointed with how its rollout is going.
Personally, I use DNS over UDP to my local PiHole which deals with all the secure DNS lookup protocols. This way only one device needs to maintain connections and deal with session resumption while every other device can rely on the simplicity and speed of UDP connections. Not exactly a defence-in-depth approach but it works well enough for me.
A real solution would be to meaningfully extend DNS in some way but doing so would require backporting this new protocol to at least ten years of computers, tablets, smartphones and IoT devices. I'd welcome a new protocol that fixes these issues if all I'd need is install another app or set up a forwarding service for legacy software, but most of the world wants something that Just Works(TM) and that Windows 7 server in the basement everybody hides when the auditor visits still needs to work.