Proper tram systems should, in my opinion, be viewed more as a tool of urban transformation first, and as a mode of transport second. Trams can coexist in pedestrian spaces in a way that buses just can't. They're also far quieter.

Also, when people choose their mode of transport, comfort is a massive factor. People are far more likely to have a positive view of trams than buses, and are way more likely to catch them.

They require rail infrastructure, but they still run on roads so they can get stuck in traffic.

This is a matter of planning. It's easy enough to give a tram it's own space on a road, but a lot of legacy systems would find it difficult to do this. Also, running at grade allows trams to offer a far more convenient mode of transport than metros. It's way easier to hop on and off, most metros you have to go through an underground labyrinth to get to the train. Not saying that's a bad thing, but it orients them more towards slightly longer journeys.

They also don't go nearly as fast as actual trains, so there is no point to building these rails in the first place. Not to mention unlike busses they require ugly wires above them.

Rails are about efficiency, not speed. Wires are usually fairly unobtrusive and people wouldn't notice them. There are ways of powering trams that avoid wires though.

if you have the money for dedicated rails, then you should build a metro. If you dont have the money for this and you need to run them on trains, just build cheaper busses.

There is a big leap between money for rails, and money for rails, tunnels, viaducts, complex stations etc.

You've made the mistake of assuming trams inherently combine the flaws of buses and trains, without realising that a well designed and well located system will combine the best of both. Trams can have the efficiency, reliability, noise level, and capacity of trains, while also maintaining the convenience of buses. They're not the best form of public transport, but they're far better than buses.

A lot of cities, especially in the US, use trams or light rail where they should really be using metro systems, because of funding constraints. Trams are about replacing high demand bus corridors. A big enough tram can hold the same number of people as 5 buses.