What happens if I increase the value from Http Maximum Header count and Http Maximum header Size

you can setup those limits, just tested on 11.6. big-ip will not pre allocate this amount of memory for each request, it will only if request is having such amoint of headers/size. So yes, if all your traffic is having thousand of headers per request you will consume more memory and potentially affecting overall max performances (less simultaneous connection for example) .

Be aware that it s a security mesure to limit buffer overflow attacks on you backend for example, of resource exhaustion.

internal db keys are also available to tell you big-ip to no reject by default if you exeed such values. you will have to ask support to get them.