What is the rationale behind requiring Wi-Fi to backup to iCloud from my iOS device? What is wrong with using 3G or 4G to backup?
Let me speculate for the logic behind the decision, since there is no published reason per @grgarside.
Making you (or forcing) to use the 3G or 4G will use your personal Telephone providers network that in all case you pay money for.
In some cases this can be expensive (depending on data plan you have), and in other cases with limitations how much can you transfer.
Using WiFi is considered open network, in many case you do not pay for it (public), and no limit how much you can transfer.
I agree Apple could make it a choice (for you to choose), but lacking that feature, the safe choice is WiFi.
Without going into speculation, there appears to be no official word on why this has been done. There are a number of iCloud Backup KB articles, mentioning that Wi-Fi is the only way to backup your device:
…however, per almost all Apple documentation of this sort, there is no reasoning to their decisions.
If you need to connect over 3G/4G - you can tether to another iOS device and then backups see WiFi and progress smoothly in my experience. There doesn't appear to be any opt-in choice to self-backup. http://feedback.apple.com would be the only avenue to ask for this feature going forward.
There used to be a limit on the size of apps you could download over the cell network - I believe 10MB was the first limit. This was put in place on the device by apple because AT&T (who initially was only offering unlimited data packages) still wanted to not have people download gigantic things over the cell network. I also believe a similar thing occurred initially with a lot of streaming apps, where if they are on the cell network they'll push a lower quality video/audio, or simply say wifi-only. All these regulations don't make as much sense anymore now that many plans are pay-per-byte, but there are still many that are not (especially in the USA)