There are differences in the capabilities of different modes, AM, SSB, FM, whatever. Each have aspects that may be of more interest to some people, and then there are 'draw backs' to all of them. One aspect of SSB is that it does have more 'range' than the same amount of power used by AM does. Could it make it easier to talk to different stations? Sure, but at the same time, if those other stations don't have SSB capability, it stops your talking to them too.
Power can be measured in different ways and still be the exact same amount of power no matter what the 'numbers' say. A stock SSB radio doesn't put out any more power than an AM stock radio does, it's just in a different form which can make a different in particular ways, more 'range' for instance.
Sure, more power can certainly make a difference, but in general, it's a loosing proposition. Mainly because of the price, and forgetting about the legality of it. To realize -any- benefit from an increase in power, you have to double the amount of power. How far can you take that before your wallet starts screaming? There are diminishing returns, it's not a 'cure all' by any means.
- 'Doc
(If you think you might like to have SSB ability, then why not? Don't think you'd like it or use it? Then why bother.)