When choosing whether or not to forgo your starter, there are multiple factors one must take into consideration:
1. Your starter's stats vs. your other options
Starter Pokemon tend to be higher than average. In their final form they have a base stat between 525 and 535, a high total for a regular Pokemon. Their stat spreads also tend to be decent. But some wild Pokemon may give them competion. For example, emboar has a lower attack and speed than darmanitan, and as such darmanitan could be considered the superior physical sweeper.
2. Your starter's movepool vs. your other options
Starter Pokemon have varying degrees of movepool viability. Consider your starters movepool. Going back to emboar, it has a wide array of coverage moves such as scald, stone edge and grass knot, which is arguably superior to that of darmanitan, though darmanitan's movepool is still quite impressive. Think about the kind if moves your Pokemon should run to ensure a high quality team. Also consider what HM's you want on the team (especially in the case of water starters)
3. Your starters ability vs, your other options
Normally this is not that big of an issue unless the ability is something like truant, but there are some abilities, like pressure, that have a handy field affect.
4. The availability of wild ______ types
Your starter might one of a few, or one of many, of its type available. Infernape, for example, is one of two fully evolved fire types in diamond, excluding heatran. On the other hand, there are typically many water types available to you.
5. Typing and team synergy
What it really comes down too is whether or not you need a Pokemon of your starters type. Grass types, for example, tend to have many weaknesses. Likewise, your starter may gain a second typing that is shared or makes it unfitting with a teammate, causing problems with your synergy.
6. Your starter Pokemons individual stats
Your starter may have a poor nature or poor Ivs. If so, It may be best to seek a replacement
7. Do you like it?
Yes that's as cheesy as it sounds. Some players see more than just stats. Some like a Pokemons appearance or personality. They're the Ashes of the world.
Well, thanks for reading. Consider these factors when making your decision. I personally stick with my starter (I'm an ash) but do what you think is right.
Hope this helped