As mentioned, this is a particularly apt piece of advice if you’re counting pennies. It’s normal to go over budget, but it’s best to try and keep overspending to a minimum so you don’t put yourself in an awkward financial position. Moreover, if you’re trying to adhere to a particular timeframe for your kitchen renovation, changing permanent fixtures will add extra time, so be mindful of this if you want it to be finished by a certain date.
As Robert Johnson pointed out, this is not the sort of task you should attempt yourself (unless you have prior experience, of course). Doing it wrong will lead to considerably more problems down the line and therefore bigger expenses even when the renovation is over. Generally, most fixtures aren’t cheap in the first place, and once you add in the labor costs and added time you may feel like you’ve made a huge kitchen renovation mistake.
Because of this, it isn’t worth meddling with permanent features unless you really have to. Still, if you are determined to get a new sink or stove, the best thing to do is to be aware of the above issues so you don’t feel caught out by what it will cost you, both literally and time-wise.