As the other replies mentioned, this is pretty standard. I think there's sometimes an exception for companies that a fund passes on, or for very small investments (e.g. if you personally invest $10k into a $5m company, then your fund's LPs probably won't care).
The main concern is this: let's say your fund passes on Twitter during its seed round, but you put $25k into it personally. 8 years later, the company has an IPO and you get a 100x or 1000x return. LPs are going to be frustrated that they let you invest on their behalf, but you took such a great investment for yourself. Even if the fund passed, there will always be the perception of "maybe they just passed so that Partner X could invest individually because the company looked very promising."
The main concern is this: let's say your fund passes on Twitter during its seed round, but you put $25k into it personally. 8 years later, the company has an IPO and you get a 100x or 1000x return. LPs are going to be frustrated that they let you invest on their behalf, but you took such a great investment for yourself. Even if the fund passed, there will always be the perception of "maybe they just passed so that Partner X could invest individually because the company looked very promising."