Porcelain Crowns Instead of Braces for Gapped Teeth?

It really depends on how big the gap is. If the gaps are large, the resulting crowns or veneers will be extremely large, giving you bulky appearing teeth. Minor gaps are routinely closed by placing porcelain restorations (veneers or crowns).
But at age 23 you should consider a multidisciplinary approach (not JUST crowns or not JUST braces). There likely has been some drifting or migration, allowing the canines to get closer to the centrals. This creates some problems, both aesthetically and functionally. The narrower arch constricts the airway (sleep apnea can develop) and the root eminences (bone surrounding the roots of the canines) are too close to the middle of your face, dramatically altering the appearance.
The BEST plan would be to use orthodontics to align the teeth better (EXPAND the arch) and create space for implants where the teeth are missing. After the canines are in place and the implants have healed, crown the implants and you will have a smile that could last a lifetime! This approach is NOT quick, but with so much of your life ahead of you, the wait will be worth it.
If you can, I would suggest AVOIDING lateralizing the canines (moving the eye teeth next to the centrals and then shaping them to look like lateral incisors).
Without seeing pictures, it is difficult to give adequate advice, but it sounds like you should have consultations with several offices to see what truly could be done for you.

I can answer both as a cosmetic dentist AND as a patient missing a front tooth as well.  As a teenager, my dentist told my parents that the best solution was to crown 4 front teeth to mask the slight space I had, which was done.  Since that time I have had these crowns replaced two more times...and I am not that old!  The most recent replacement I had was just this year, after having braces to better align the space of the missing tooth, and now my smile looks TERRIFIC!

 In my opinion, closing the spaces with crowns alone never looks "quite right." The face looks too narrow and the bone supporting the canine teeth doesn't have the right shape for that area of the smile. The jaw can also become narrow enough to create problems with breathing and jaw joint function, which over time can lead to snoring/sleep apnea, and jaw joint disorder (TMD)...all significant medical issues.

My recommendation for patients "in my shoes" is to first have orthodontic treatment (braces) to properly align the teeth, widen the jaws, and leave even spaces for the missing teeth. Then depending on your age, smile, gum and bone in that area...either have implants placed to replace the missing teeth, or bridges if implants are not an option. 

Have a consultation with a good cosmetic dentist in your area, as well as with an orthodontist recommended by that cosmetic dentist, and good luck!

The condition of missing the Lateral or "side" front Teeth is not that uncommon.  Without seeing your specific case my concern is the AMOUNT of space you have between your two Front Teeth and Canines. If the space is too large your new Crowns would appear too wide creating a very undesirable smile. If the canines have drifted or migrated toward the centrals the canine root eminences will be too centered and again giving you an appearance you ultimately would not be happy with. Since you are so young please be motivated to seek out the best possible solution that would be effective in giving you the ideal Smile and Function you need and deserve for your lifetime. An initial exam and x-rays are so vital so esthetic previews can be generated to give you projected outcomes! An Orthodontic Consult is also a must!.Based on your specific situation some minor expansion and other minor tooth movements would probably put you in a better position for a more desirable long term outcome. After this is addressed its also possible that 2 individual Implants may be the most conservative yet effective solution to help you regain your ideal smile!