As mentioned by others, Belgrove Street is topped up by staff supplying bikes from a nearby storage point. If you are there at 7:30, you will see the hundreds of bikes in the storage unit and stacked up outside, being brought into the racks by the team of people there.
At this time of year by 8:05 they are down to a couple of dozen and by 8:20 there will be none left. In the summer they disapeared earlier and in mid winter they may last longer.
Don’t bother with Chad Street, as they only fill that up when Belgrove Street is out of order.
In an evening staff arrive at Belgrove Street around 17:00 to start emptying the racks to store away for the next day, so there should be no problem dropping one off there.
So the fundamental problem is the service doesn’t suit you, and the particular times that you travel. And even if they fitted in with your travel times, and on filling up Belgrove Street with bikes to 8:20 that still wouldn’t help you, as you have already said that there is nowhere to dock it at the other end. And the reverse problem in the evening.
Frankly without a massive increase in redistribution, then it is impossible that everyones demands could be met, and quite frankly it would probably be cheaper for them just to pay for a taxi for everyone.
As for the bikes not being “designed for commuting”, that was part of the design brief, that it would be impossible to cope with the vast numbers of commuters without either having vast numbers of docking points at stations, and huge amounts of redistribution to deal with the tidal flow.
The problem is that when the scheme was launched it was for subscription users only, and PAYG users were only allowed months later. Subscription users tended to be commuters, and although the scheme wasn’t designed for commuters, they had to deal with them as they were the only customers, and if they didn’t the press would have had a field day.
Although I am a commuter comming into Kings Cross and use Boris Bikes, personally I think that by trying to redistribute they are making a rod for their own back by raising expectations, and it might be better if they didn’t do anything at all.