One way flight w/ layover - 1 ticket vs. 2 separate tickets

Would we have to go through customs in London and then check back in through security, etc?

Yes, you would (not "customs" but passport control; customs is typically just walking through a door); and yes, you would probably need to clear security, too.

Does anyone know a reason not to book two separate flights?

Well, if you miss your onward flight, you need to buy a replacement ticket on the spot - that's one reason. The consequences of having that happen would be less on your outbound flight; on your return flight, it would be expensive (how expensive? go look at what same-day tickets cost).

Would we have to go through customs in London and then check back in through security, etc?

Do you plan to have checked bags?

One way flights are often a costly way to buy international travel. Are you not coming back? If so look at doing 'multi-city' ( aka open jaw) bookings, not one-ways.. Does anyone know a reason not to book two separate flights?

. Does anyone know a reason not to book two separate flights?

Yes. If the 1st flight is late and you miss the 2nd flight, you get to buy a new ticket to complete the journey.
If you have a single ticket, the airline would be responsible to get you to your destination at no additional cost.

The downside of booking two tickets separately is if your initial flight to London is late enough to cause you to miss your onward flight to Venice, you will be out the cost of any nonrefundable ticket you bought AND you will then need to buy a replacement ticket at an elevated price since you will be buying it at the last minute. If you buy tickets that are refundable/changeable you will have some options, but you could be competing with other travelers to snap up onward tickets to Venice at the last minute.
Because BA could sell you a nonrefundable ticket months in advance and then cancel the flight just days before the departure date— buying two separate tix from different airlines is not a risk I would take. BA would have to refund you the amount you paid for the cancelled flight, but you could find yourself scrambling to buy last minute replacement tickets at much, much higher prices than the original price you paid. And then you’d need to figure out if the London to Venice ticket would still be usable.
It would be a helluva way to begin a vacation.
Have you checked a website such as www.Skyscanner.com to see all the flights from Baltimore to Venice that are offered? With a comprehensive listing of options, you’ll likely find one that works better for you. I know you just want a one-way ticket but just to give you an idea of what’s available—Delta Airlines has 13-hour April flights from BWI to Venice that connect in Atlanta for less than $900 roundtrip.
Austrian Airlines has ten-hour one-way flights from Washington Dulles Airport (IAD) to Venice with a 40-minute layover in Vienna. Skyscanner shows all the consolidators selling these tickets with reputable Trip.com selling the tickets for $580. per person.

Here's another consideration that just happened to me. I have booked 2 one-ways to Europe (3 weeks apart) for this July (a very long story) that was more expensive.
Just yesterday I heard from Delta that the first flight of 2 back to the US was moved back 4 hours, for a 6 a.m. departure- I also now have an 8 hour layover before boarding flight #2 to the US.
OTOH, what if flight #1 was moved 4+ hours ahead plus the other moved back 4 hours? At least booked as one ticket I would have had recourse to eventually be put on a flight.
That wouldn't be true with two separate airlines booked as two separate tickets. I can't think of any flights recently that haven't had the departure times changed, sometimes significantly.
So the caveat is to factor that into the equation, too. Sometimes ( and I have a couple times) you get lucky and it does work- but there's so many variables over which you have no control.

It could be there would be no problems if you do a carryon versus checking a bag. On the other hand, it could end up costing a lot more money and your time than the ticket with connecting flights. And frankly, the amount of hiccups that seem to be occurring with flights during the last year, I personally would not want to take that chance but that’s just me.

I was just faced with buying tickets for the Spain tour from Seattle. Since I like to visit London, I did a round trip to London, then from London a multi city ticket to Barcelona and back from Seville. That way I get time in London pre and post my Spain tour AND the two tickets were considerably cheaper than going straight to Barcelona from Seattle.

As that great philsopher Clint Eastwod once said..."Do you feel lucky, huh, do you?"

Thank you to all for the helpful replies. You have confirmed my suspicion that the savings are not worth the gamble.

Is there a reason you are buying a one way ticket? Not coming back?

But in your original question, there is risk if you have not allowed much time, I would likely spend a night or more in London, flying out a different day.

What if you traveled the first leg a day early - will you save enough on the 2 separate tickets to pay for an overnight before the flight in Europe?

I decided to book two separate tickets to get to Spain via London. AND I decided to stay in London for a couple of days as it's a great place for me to get over the 8 hour time change. The hotel price was basically covered by the difference in getting one ticket (just a layover to change planes in London).