The concept of token has a number of benefits and drawbacks but for the purpose of your question, I would only list some of the drawbacks that I am aware of:

• Lock period: Staking locks your tokens for a period of time which means they're illiquid at that time and you can't use them for anything else. While this is just like holding tokens, the problem lies in the fact that in most projects, there's an unstaking period anywhere between 1-4 days. In that time, you will most likely earn zero rewards and tokens remain illiquid for that period. So in cases where you want to readily sell (if there's a bad PR for the token in question) you can't immediately sell.
• Supply increase and dilution: These staking rewards adds to the total supply and results in dilution of those rewards (in most cases, the token loses value).