I'd say terrible idea for one main reason.
If MS starts next gen and says here's next gen and it's $499 or $599, and PS5 is somewhere in that mix, and then they come out 6 months to 12 months later and say here's another next gen console and it's much weaker, people are going to be like WTF?
Mid gen upgrades can make sense. A downgrade makes little sense. Removing a disc drive doesn't really change how the game plays, so that is more acceptable though.
*The only way it makes sense to me is if MS overshoots at $599 and PS5 is $399. Then MS has an excuse to drop another console around $399.
Lockhart will not be aimed at the buyer who is going to pay 499 to 599 for either system. Lockhart looks to aim price and performance wise for the very price conscious consumer which is the people who look at purchasing a console around the 299 mark. I believe you are looking at this like its a sprint but I believe they are looking at the situation as a marathon. I believe MS should agressively target the budget console and loss leader it at 299 instead of your premium console which if sells at X1X starting price will only get hardcore gamers to spoon up in the early years. Starting later allows MS to agressively price the cheaper console at a competitive price and performance to the PS5.
Also why would people who purchase a console at a budget price say WTF. Its a console for the budget buyer who wants in on next gen without the high dollar amount. MS still have the premium beast and the lower cost system isn't considered a mid gen system. Its considered as a budget system which is something different the market hasn't experience yet. Testing how this goes will be critical if such designs will be fruitful in the future.
The only way MS can release Lockhart at the same time as the Series X if they already know Sony price point and performance with the PS5 on release. Lockhart has to perform at a specific delta and price point to be viable alternative, especially if its weaker than the PS5. It has to perform at such a level to not make that much of a difference but still give the gamer next gen features and performance at a reasonable price.
Some would just buy it at $299 without question. However, many who wanted and were saving up for a last gen console are going to be really confused, not to mention present gen owners who are looking to jump into next gen.
MS will almost certainly have to discontinue XB1X. That's a "beast" of a console at 6TF for around $399 pricing maybe? Then MS is going to launch Lockhart at $299 a year later and say it's next gen and better than XB1X was? You'd have to be a complete moron not to question that, and when MS simply says it's just new tech and that's why, many aren't going to completely buy that explanation, even if it's mostly the truth. They're either going to think MS was ripping people off with XB1X, or that Lockhart isn't really a next gen console. Which at $299, it will be borderline next gen at best.
The average person is going to simply think why not just keep XB1X and drop it to $299 or less? Why are you trying to make us buy another new console, and with lesser specs? Why was the old version so much more expensive? Etc. That's not something MS should want to deal with. The longer they allow XB1X to exist next gen, the worse it'll be. If Lockhart drops at the same time as XBSX, and XB1X is off the shelves by then, it will be much more clear to people it was done for legitimate reasons. It won't stop some people from questioning it still, just like how some people will just buy it regardless, but mitigating future push back would be worth it, especially at the start of a new gen. They know what it can do to a brand based on XB1.
The smart move would be to design the console to be a $349 cost to MS. Then decide what to charge at launch. If PS5 is $499, then leave it at $349. If PS5 is $399, then price Lockhart at $299 and eat $50 on each unit sold.