Deploying LTM, GTM and ASM on the same appliance?

It depends ;-)

I think LTM + GTM is quite reasonable but ASM tends to consume cpu resources quite a bit and can cause issues. You would have to think in terms of what are the main pain points you are solving. I mean, some applications/accounts tend to be targeted for DNS based DDoS/DoS and in this case, having a separate GTM helps as you are not sacrificing your LTM or ASM when there is a DNS level attack. What kind of signatures are you intending to utilize on ASM is important too as some signatures can consume a lot of resources. Do you have access to an F5 SE - might provide a better answer based on your unique needs.