Based on my own experience there are probably more factors involved than that. Liners have never given me an issue, but I wouldn't recommend installing them in tires that are going to be run at low pressures. that means IMO that your 45PSI is marginal and if the pressure drops just with regular air loss you'll run the risk of the tire and liner rotating on the rim under heavy braking. Personally that's my opinion of the circumstances that can cause issues with liners and was probably a factor in people that had cuts from liners. Likewise, without a liner, low pressures will give the tire AND tube an opportunity to rotate and occasionally rip the valve stem out of the tube.

I've routinely installed thick-walled tubes (some come with a sealant already installed) on electric bikes where its a real nuisance to change a rear flat. They work well, but glass slivers are hard to stop. As some other posters have already mentioned - a Kevlar belted tire is probably the best solution to that kind of issue, but they're not cheap and unless its a consistent problem, I personally couldn't justify the additional expense. High performance tires like Schwalbes can give a lot of mileage, but most people I've seen have had to change the tires while the tread depth was still good simply because they stored the bike outside and UV damage after a number of years resulted in the rubber crazing and literally coming off the tire in chunks. I'm using VeeRubber City Wolves ($15) on my own hybrid during the summer. I'll probably get about three years out of them, but my bikes get stored inside..

A glass sliver doesn't usually scrap a tire and a new tube is probably only $5. In my own area, I ride with a kit that includes a spare tire, tube, tire leavers and CO2 cartridge and have never needed any of them on the road in 10 years. No liners in any wheels, but I'm also pretty much on bike paths almost continuously. Your neighborhood may be completely different.