Why Peukert's law is always ignored in battery(lead Acid) guides available on Internet?
1 KW requires 4.54 current for a single phase at homes in Pakistan
  (220 AC at 50 Hz). This current can also be called discharging current
  of battery.


Not unless the battery is a 220 volt battery. If it's a 12-volt battery (as JRE commented) then for 1 KW you need about 83 amps. Power equals voltage times current, remember?

Then 3 kWh requires 3 x 83.3 amps, or 250 Ah. Assuming a 50% discharge limit, the battery capacity required is 500 Ah.


  Is it economical to use such a huge battery for only 1 KW load?


Well, that's up to you, isn't it? How badly do you want to provide that 1 kW load? What is the price of the alternative?

And, for what it's worth, as pjc commented 1 kW from a battery system is a very large draw. It's made worse by your miscalculation of the required current, too.

Now, as for your original question about Peukert's Law, the answer is pretty simple. It is ignored because it's not particularly useful. When designing a battery system the load is hardly ever precisely known, so attempting to precisely define battery life is pretty much a hopeless cause. And that is before adding in the effects of varying temperature and operational life. So what people do is use the "standard" ratings and, particularly if the load current is expected to be high, add a safety factor. The situation is made even worse by the fact the charging efficiency decreases as a battery reaches full charge. And that effect is also affected by charge current level, temperature and battery life.

Battery performance is nastily complex to calculate, so nobody does.