The output of the inverter will always be less than the input from the panels. It's not a magic box that breaks the laws of thermodynamics
If I understand the issue you are discussing, you are saying that 1 kW of solar panel will only produce 1kW of electricity for a very short portion of the day. Further you state that for every 1kW of DC entering the inverter, less than 1kW of AC will exit the inverter. You are then using this to claim that the inverter output will be at its peak for only a very short portion of the day.
The first point is correct. Unless your panels are on a tracker, they will only produce peak rated power for a small portion of the day.
The second point is also correct. Inverter efficiency is always less than unity.
But the claim about inverter output relative to its peak is not correct because it misses a key factor: inverter DC to AC ratio.
It is very common for the DC rating of the panels to significantly exceed the AC rating of the inverter. Inverters have separate ratings for maximum DC panel capacity and maximum AC output, with the DC rating greatly exceeding the AC rating. When the AC limit is met, the inverter adjusts the DC voltage so that the panels are not operating at their maximum power point. The reason for doing this is to maximize the energy production vs the total cost of the system; inverters are not free so it makes sense to loose some of the potential production of the panels in order to better use the investment in the inverter.
But what this means is that the inverter will be running at maximum AC capacity for a greater portion of the day than the panels are running.
To take an extreme case, imagine a 10kW PV array connected to a 5kW inverter. The inverter will be at maximum output once the panels are at 50% of peak insolation.
More realistically the DC:AC ratio will be in the range of 1.2-1.5.
-Jon