Depending on your local laws, and in any state that has adopted CA emissions regulations, you'd be in violation of the law.

In an engine replacement, ie 72 225 for a 78 225, the emissions neccesary to be legal depends on either the date of manufacture for the body or the engine, whichever is later. So a 77 225 in a 72 Dart would be required to meet 77 emissions requirements, however, you cannot run a 72 225 in a 77 vehicle, engine has to be at leas teh same year or newer than the body. The ONLY exception is catalytic converters which are solely body dependant, fire hazard in a body not originally designed for it.

If your state doesn't run CA emissions, which is most, you will have to find out what the law states.

As for "emissions exempt" that means you are exempt from testing, only. Federal law, at the minimum, requires you to keep an maintain the stock emissions equipment. I do not, however, know what the feds require when doing an engine replacement, at the minimum I would guess whatever the emissions you original setup had.

As for an engine swap, ie a 440 in place of a 225, then it has to meet the requirements for the year of the body it's being swapped into or the year of the engine, it also has to be a pass car engine, if it's swapped into a pass car, and it has to be an available option in a pass car for that year. So no, 426's in a 73 Newport.

You can swap a 360 in place of a 318 as it's considered a replacement, not a swap. But it still has to meet the year criteria and have the appropriate emissions retained.

As for removing emmisions equipment to make it run better, wrong. Most have no net effect on power, some have a benefit if you use it. Granted, back in the day cats were restrictive, but they no longer are. Egr keeps ping under control allowing more dynamic compression for more power.

as for the argument of why "guys" don't run EGR if it makes more power, heck look at this thread and you'll see the answer, lack of knowlege about what it does and how to take advantage of it.