"Isn't this technology a spread-spectrum thing? Why can't they give the same block of spectrum to all the operators, and let their use of it be determined by the number of customers they have? "
CDMA-1, EVDO, FOMA, 3G/HSPA/UMTS/W-CDMA and CDMA2000 are all spread spectrum. There is no free lunch. Google Cell Breathing. On 3G each operator uses 3 x 5MHz + 5MHz separate channels, or it would be rubbish.
LTE is like DAB, WiMax, DTT , it doesn't use Spread Spectrum, but OFDM.
The off quoted 100Mbps is for ONE user only connected, in one sector, on a 20MHz + 20MHz channel with a perfect signal. Cell Edge is 0.6Mbps with only a SINGLE connection in Use.
To make a cellular network you need a minimum of THREE different channels, and 6 or 9 is much much better.
To get more capacity you need more channels or much smaller cells. Random isn't evenly distributed. So with smaller cells and more operators, it's more likely some have too many people and some have only 1 or 2.
various nearly accurate Wikipedia articles on all this too.