What are the trade-offs between polymerase chain reaction (PCR) vs Loop-mediated isothermal amplification (LAMP)?
Having to use more primers is definitely one of the big reasons. Primer design is difficult and time-consuming, and even more so if you're dealing with similar targets. For instance, if you're trying to differentiate closely related bacterial strains, having to design primers for 6 or 8 regions instead of just two is going to lower your ability to differentiate the strains. It's even worse if you're working with viruses - these mutate quickly and therefore your LAMP primers will fail to amplify the virus sooner than normal PCR primers. 

LAMP is good because it's cheap and portable, but there are portable PCR thermocyclers starting to be produced (eg. miniPCR, Biomeme) and so diagnostically speaking, it's a lot easier to just use existing PCR primers that have been validated and are widely used, instead of creating new primers that you'll have to validate all over again. 

The primers again are important if you're trying to amplify multiple targets - it's a lot easier to create degenerate or consensus primers for a standard PCR than it is for LAMP, and also easier to distinguish multiple target bands on a gel, which isn't possible for LAMP. 

It can vary, but in my personal experience, I have always found Taqman-based PCR to be more sensitive than LAMP. You can't use Taqman probes with LAMP. You also can't use LAMP for cloning, and melt-curve analysis isn't possible with LAMP, which is useful for detecting primer dimers and diagnostically for distinguishing between targets.  

So, LAMP is good because it's cheap, requires less equipment, can be done in the field with minimal reagents, and tends to be more robust than PCR as it is less prone to be affected by inhibitors. This means it is great for in-field diagnostics in developing regions. But there is a range of things PCR can do that LAMP can't, and the complex primer design alone will prevent it from overtaking PCR.