There are 2 reason: providing protection against Sybil attacks and rewarding nodes (i.e. the “servers”). From the whitepaper you linked:

This staking system provides a defence against Sybil attacks by limiting attackers based on the amount of financial resources they have available. The staking system also achieves two other goals which further reduce the likelihood of a Sybil attack. Firstly, the need for attackers to buy or control Session Tokens to run Session Nodes creates a market feedback loop which increases the cost of acquiring sufficient tokens to run large portions of the network. That is, as the attacker buys or acquires more tokens and stakes them, removing them from the circulating supply, the supply of the Session Token is decreased while the demand from the attacker must be sustained. This causes the price of any remaining Session Tokens to increase, creating an increasing price feedback loop which correlates with the scale of the attack.

The other advantage of a staked blockchain network is that Session Nodes earn rewards for the work they do, paid as Session Tokens from the Session Node Staking Reward Pool. This system makes Session distinct from altruistic networks like Tor and I2P and instead provides an incentive linked directly with the performance of a Session Node.