Consider why having bonuses spread out is good. Classes generally fall into one of two categories, they either depend on one ability score for everything (called a SAD (single-ability-dependent) class) or depend on more than one ability score for everything (called a MAD (multi-ability-dependent) class).
For MAD classes, having the bonuses spread out is important, because it means you can start with very good (16 or higher) scores in your two most important abilities, or can go 16, 16, 14 (by doing a 15 and two 14s) if you need three abilities (or if you're hyper-optimizing, play a Triton and have three 16s and three 8s at the start of the game, really fun build for a paladin). However, if you've only got a single +3 to work with, you cannot have more than one ability over 15 at game start. This is huge for classes that actually need multiple abilities to be good to do well, because it means that they're underpowered relative to a +2/+1 (or +1/+1/+1) bonus up until level 4, but at that point they're still underpowered because they have to use their ASI or Feat to shore up their lower score instead of boosting their most important one.
For SAD classes, it's actually still helpful to have a +2/+1, as it lets you start with 17 in your key ability (and thus use either an ASI or a Feat to get it to 18 at level 4) and still have a secondary skill of your choice (usually DEX or CON) in the 14-16 range at game start, which helps you either survive or be better overall. Essentially the same issue arises here as for MAD classes. Playing a spellcaster, you can easily optimize for both casting and either having a decent AC (by putting DEX at 16) or being good at concentrating (by putting CON at 16) if you've got your bonuses spread, but you can't do that if you've only got a single +3 to work with.
If you look at a large sample of characters, you can kind of see this play out a bit. Most players won't actually start with a stat at 17 (the highest you can start with with a +2/+1 race), they'll start with two at 16, or more commonly one at 16 and two at 14. That common case actually is doable with a single +3 bonus, but anything more optimized than that for multiple stats is not. As a result, by using races with a +3, you're zoning people out of optimal builds for MAD classes if they pick that race.
This may be fine, but overall it means you will not see any serious players using that race for anything but SAD classes (and even then probably mostly for glass-cannon style spellcasters, because they can't shore up their defenses as well).
The probably bigger issue here though is how this affects your class DC, which is especially important since most SAD classes lean very heavily on effects dependent on their class DC. D&D 5e is built on a concept known as 'bounded accuracy' or 'bounded power'. Effectively this means that there's an upper limit to the potential power level of any character in game, and the players approach that at a fixed rate proportionate to their level (actually it's not really a fixed rate, it's more logarithmic, as the difference between level 1 and 2 is much bigger (due to HP scaling) than the difference between most of the other levels). This is, in general, founded on the assumption of using the point buy system. That's half of why 5e only has the classic approach of rolling your scores as an alternate rule instead of the 'standard' approach (the other half is that it normalizes out overpowered (everything 14 or higher) or underpowered (everything 13 or lower) builds that sometimes arise from rolling for ability scores).
However, starting with an 18 kind of throws that off, because your class DC is now 1 higher at level one than it would normally be, and at level four it ends up being again 1 higher than it would normally be. This means that content that was designed around the 'bounded accuracy' principle (such as pretty much all published adventure modules for 5e) will be measurably easier for SAD classes and especially casters at early levels.
Whether this matters or not is largely up to you. Regardless of how you handle it, you will skew the balance of the early levels more in favor of SAD classes (either you don't correct for it, and SAD classes are more powerful, or you do, and MAD classes are weaker relative to the content than they normally would be).