I nearly agree with @phlsmk's answer, but with some small differences.
First off, the delta of a digital is not "zero everywhere except at the barrier where it is an impulse". This is what it is at $t=T$. before this, it is smoothed out, exactly like a regular option is.
The problem is on what the delta may become. This is not the only place where it happens.
Let's look at an example, just a vanilla call. K=100, r=q=0 (i.e. no drift, fwd is whatever the spot is), $\sigma$=20% (changing the vol. in all these examples will just be like changing the time, so it doesn't really make a difference to the answer). Below,
adu is absolute delta/unit, and
aguu is absolute gamma/unit/unit.
note how as the time goes to zero, the payoff approaches a cusp. Here are the delta and gamma:
Now, i think it's fairly easy to see that as $t \to T$ this becomes unmanageable to hedge.
One method to deal with this is to break up the option into several, with different strikes spread around the original one. Here's what that looks like (with the $t=1.0$ pv overlayed in orange for comparison):
and here's the difference in price as time goes on:
Okay, so delta and gamma?
So the delta has an extra step in the middle, and the gamma is still spikey, but now each spike is half the size of before. Obviously we can do better still.
Let's do a strip of options spread from 90 to 110.
Here's our new payoff, and the comparison to the original:
And again, delta and gamma:
So, you can see that by spreading out our payoff, we can reduce the potential risk we may face in the future, with only a minimal increase in cost.
This is just for a vanilla option - but a digital is essentially the first derivative of a call wrt. strike, so just swap gamma for delta in the examples above.
Obviously the more you smear out the barriers, the higher the cost will be. This is where risk limits come in. If you want to do one of these trades in small size, there is no need for this, since the maximum risk will be small. If you come to me and ask to do a 100mm digital though, then i could potentially have a very large hedge on my hands, so i will smooth the payout to reduce that risk - this is just another cost of doing a large trade. If you can find someone else who is happier to accept enormous risk, then perhaps they will offer you a lower price.
I disagree that doing this will make your prices non competitive, as it is an extremely standard thing to do -> everyone does it. How much may differ, but as i mentioned already, this is also dependent on size. And as you move to larger size, the market is going to shrink anyway, so you're going to expect costs to increase.
And for the barrier shift - why would the bank ever do this in any direction other than against the client? When done like this, the PnL at expiry is always $\geqslant0$.
so, i spent a little longer toying around with my spreadsheet for this - you can do even better. Why weight the notionals of the options evenly? If we weight them according to a normal, we can get nicely behaved greeks all the time, even at $t=T$:
where that last one is the delta of your digital. Notice that the two methods are different - the first has a lower level for the whole region, but it appears abruptly. the second has a larger maximum but approaches slowly. Which you decide to go with will depend on how you want to manage things.