It's frustrating as the online statements we have look almost exactly the same as those we received in the post - all that is missing is a QR / barcode and some number / letter code along the top and side of the page. All of the relevant names, dates and address info is on there.
Would it help if we printed these and took them to the bank to get them stamped / approved as originals?
It is very frustrating, but unfortunately, using online statements defeats the object of the correspondence requirement.
It's not about just having statements/bills in your names, it's about showing that they were physically delivered to your house in the months that they were issued, thereby 'proving' that you were both physically present in the house on those dates in order to receive the paper copies in person.
Online statements are not definite evidence that you were physically living in the house on those dates, because:
a) you didn't receive a hard copy of them on the dates they were issued
b) the address on your bank statements might be different to the address where you actually live... for example, you might have started out living with family members and forgotten to change the address on the account when you moved.
As another example, I have a US bank account which is registered to my aunt's house in the US, for which I get online statements only.
Does that mean that, if I print them out, they can be used concrete proof I have been living at that address in the US for the last few years? No, they can't. They are not proof of anything, because I do not live in the US and I have not lived in the US for 12 years (I have also never lived at my aunt's address... I was living 2 states over).
Now, if the US bank issued paper statements only, in theory the only way I could get those paper statements would be if I was physically living at that address in the US and therefore I was there to receive those statements in person.
Of course, that reasoning isn't completely foolproof, because my aunt could have mailed all the paper statements to me in the UK, or I could have picked them up when I went over to visit her... but paper statements are the evidence that UKVI uses to determine whether or not you have been living together for the last 2 years.