Acid does alter the concrete in that it dissolves the calcium while not really affecting the other components, such as the aggregate materials, gravel, etc. When the calcium is gone there are tiny voids left in the concrete's surface, those tiny holes act as anchor points for the subsequent coating to slip into, promoting better mechanical adhesion, and, with quality coatings, superior chemical bonding as well.
This etching process doesn't penetrate that deeply, so it doesn't compromise the overall strength of the concrete much, generally not enough to be near a concern. If the point of etching is to prep the surface for an epoxy coating, then the protection that epoxy coating provides will more than offset any "damage" the acid etch itself caused.
Acid etch can have downsides. Muriatic (aka hydrochloric) acid, probably the most common acid used in floor prepping, is a very strong, caustic, chemical. It can damage metals, even ones it doesn't come into direct contact with. Additionally it has health and safety risks, as well as a very powerful and unpleasant odor. After it's done its job it needs to be neutralized and the area thoroughly rinsed before apply any coating.
Fortunately there are other chemical alternatives that provide identical etching action - but without the nasty side effects. We often use them on projects where there are people, animals or property that can't be exposed to the harsher acids and/or dust that mechanical profiling entails. Zoos, research facilities, clean rooms, restaurants, food or chemical prep areas, patient care facilities, metal framed buildings, etc. There are different alternate chemicals available, some are just a bit milder than muriatic acid, while the more sophisticated solutions (like our OrganiPrep 921) are far more benign than muriatic acid, but just as effective.
Shot blasting is overall probably a better method to profile the concrete, and it can go very quickly, but it's not without drawbacks. For the DIY project shot blast equipment can be difficult to find, and when it is located the rental price can be steep, although sometimes it's relatively inexpensive (recently reported rental rates have ranged from $110 to $400, for identical set-ups) in other words - availability is unpredictable.
Most rental shot blast systems have an attached vacuum unit to mitigate dust, and with a shop vac, or good wash down, dust shouldn't be an issues, but in some situations even a small amount of dust is unacceptable.
There is also a bit of a learning curve with the equipment and process. Depending on the condition of the floor, and the skill of the operator, it can be easy to "over blast" an area. If the blasting does take off too much material, it may require additional repair work to smooth the concrete enough to coat it.