Diversification applies to startup investing because historically the majority of returns have come from a small number of companies. Returns on startup investments are usually unevenly distributed with a large part of returns hailing from a small number of investments. While hard to grasp, it is not unusual for the return of one company to be bigger than the rest of the startup portfolio investments combined.
In theory, the more you spread your investments out across many companies, the more likely you are to invest in companies that will be successful and generate a return. While there is no guarantee that diversifying your investments will lead to a good return on investment, the general consensus is that diversifying your startup portfolio should lead to better returns as opposed to not diversifying.
However you need to also bear in mind that even if you invest in a large number of companies, diversification will not necessarily save you from having poor returns in your portfolio.