FeralFly

Good point. Anything that targets a DCV 3 or zeroes out the target's DCV becomes that much more useful.

3d6 is also easy to work out exactly.  There are exactly 1, 3, 6, 10, 15, 21, 25, 27 ways to roll 3-10;  flip side, reverse that to roll 11-18.
  
3:  1 in 216 (0.46%)
4-:  4 (1.85%)
5-:  10 (4.63%)
6-:  20 (9.26%)
7-:  35 (16.2%)
8-:  56 (25.93%)
9-:  81 (37.5%)
10-:  108  (50%)
 
So 11- is 62.5%, 12- is 74%, etc.  
 
So one thing this will do...is draw combat out, because misses become notably more prevalent.  11- is 5 out of 8;  10- is 4 out of 8.  If we use a SPD of 4, that's 1 strike every 2 turns.  It'll matter.  And as Derek notes, there are ripple effects.  This would make, for example, AoE 1 Hex attacks a tad more attractive, because you're only hitting a DCV of 3.  Even a -2 OCV Range Mod is getting VERY painful, as would multiple attack penalties.  Autofire...multiple impacts is based on how well you make your roll, so you'd be consistently getting 1 less.  LOTS of things change.

It does, but I would also add, the amount of change you'd get in the results (even if you and your group think it would be a good change) almost certainly wouldn't be worth the effort involved in re-jiggering the system to shift the core mechanic by one.  You could just simulate this effect by applying an automatic -1 to all Success Rolls across the board, rather than actually recalculating them to a lower base.  However, that might get things out of whack with other parts of the system in ways that aren't immediately obvious, because they're presuming you're using a base of 11.

?? 10- is 50% and 11- is 62.5%.

I already had the stats, but https://rumkin.com/tools/die-stats/#!/?dice=6d6D1 can confirm (great site that @unclevladreferred me to recently).
 
Definitely makes success less likely.  Whether that's good or bad depends on how you prefer your game to play - maybe the players want to be missed more, and are prepared to accept missing more often themselves as the natural result.
 

The chances of rolling 11 or less on 3d6 is about 57.87%, it is 48.15% for 10 or less.  So that means you have 9.72% less by reducing the target number to 10.   Many of the rolls in the Hero System are actually calculated.   Most skill rolls are based of the formula of 9 + STAT/5.   That works out to an 11 or less for a STAT within the 8-12 range.   You have a 25.47% chance to make an 8 or less roll.   Your chance to roll a 7 or less drops to 15.74% and quickly gets worse as you go down the chart.   When you get to the point you need a 3 to succeed you are down to a .046% chance of pulling it off. 
 
What is going to happen if you change the base to 10 is that you are going to see a lot more failures.  With the way things stand you succeed slightly more than half the time.  Dropping that to 10 is going to mean you fail more often than you succeed.     An 11 or less roll is supposed to be something that is not that hard to achieve.  Most people under normal circumstances should be able to make the roll.  When you reduce the base chance, you probably need to reduce all the rolls by the same amount.   That gives you very little leeway for having things that are moderately difficult.   Personally, I think this is a bad idea and will make the game a lot tougher and less enjoyable.