I have a good idea of where those missing messages are. They’re in a dark, sad place I call iMessage Purgatory. It is where some messages go to rot when iPhone users do the unthinkable: switch to an Android phone.

For the last week I have been living with the Google Pixel 3 (see our full review here), and I can tell you how great a phone it is, but what I really want to tell is that Apple AAPL -1.48% has erected some high walls around its iPhone users. Between that and the fact many Americans do love the Apple ecosystem, few try to leave the fortress.

Loyalty to Apple’s iOS is at 89%, according to a new study by Consumer Intelligence Research Partners. Android has an even higher loyalty rate of 92%.

Those who wish to leave iOS have to do some climbing—like buying new charging cables and transferring photos and other cloud-stored goodies. The biggest barrier, however, comes in the shape of a big green bubble. That is how Apple users know they’re chatting with someone on a non-Apple device. If outgoing messages are green, they’re not being sent via Apple’s iMessage platform; they’re just plain, old text messages.

That means no acknowledgments when a message is delivered or read—or that someone is typing a response. It also means limited video sharing and visual tools, and less, if any, compatibility with the more advanced iMessage apps, including Apple Pay.

I realize this sounds like the ultimate #firstworldproblem, especially in an age where cross-platform messaging apps seem to multiply faster than ants on a spilled Frappuccino. But getting your entire family to Disney World really is easier than getting them all on a different chat service. Plus, if you don’t pay attention to the details, you could lose precious communication with your loved ones.

How iMessage Works

Two things to know to pass iMessage 101. First, if you send a message in Apple’s Messages app from one Apple device to another, it appears on screen in a blue bubble, indicating it is being routed through Apple’s servers and encrypted end to end. This happens whether you’re logged in with your phone number or email address.

Second, if you’re sending a message from an iPhone to phones running other operating systems, it will go out in a green bubble, via your phone’s cellular network as an old-school text message (aka SMS or MMS).

iMessage exists because, well, text messaging sucks. One of the fathers of iMessage, Scott Forstall, Apple’s former senior vice president of iOS software, told me that the system was developed in the early days of iOS because Apple wanted “messaging to feel more like a conversation.”

That is still what makes blue-bubble conversations so much better than green-bubble ones. Not only do you get more functionality inside the messaging window, you can pick up the conversation from one device to the next—iPhone to MacBook to Apple Watch.

It also means things turn into a nightmare hell ride whenever I assign my phone number to a non-Apple phone.

How to Move Out

Breaking the iron grip between you and iMessage is a multistep process.

Before you switch to an Android phone, even before you pull out your SIM card, you need to disable iMessage by going to Settings > Messages, and then turning iMessage off. You can also visit this Apple support page and deregister your phone number.

But here’s the rub: Some parts of the process can take up to several hours to complete, during which time messages—and adorable niece photos—may be unable to be sent or get lost. Senders may get a red exclamation point telling them the message didn’t go through. Meanwhile, nobody might notice you’re absent from ongoing group chats.

To pre-empt that, you can initiate a new group text message, but it will limit everyone in the group to basic texting functionality. Plus, you may get the dreaded forked iMessage chain.

You also must turn off or sign out of iMessage on all your other Apple devices. Even if the other devices are logged in with just your email address, iMessage might still route them messages that you want going to your new Android phone. I had one lone iPad that was out of power but still on iMessage. When I booted it up midweek, I witnessed a modern-day Rip Van Winkle moment: There they were, all the messages I’d missed.

How Apple Can Fix It

My best advice to those with green-bubble friends or family is to move over to a better cross-platform messaging app. Facebook Inc. -owned WhatsApp is fast and has end-to-end encryption, read receipts and all that other fun stuff. So far, it has no ads either. But if you’re wary of Facebook’s abrupt product changes and moneymaking schemes, go with Signal. It also does end-to-end encryption, and you can set messages to expire after a certain amount of time.

But given the dominance of iMessage, especially in the U.S. market, it is on Apple to make the experience more inclusive. Here’s my three-pronged pitch:

Improve iMessage tech support. The most pleasant part of my lost-message distress calls to Apple tech support? Listening to Tom Petty’s “Learning to Fly” while on hold. One technician told me I should contact Google or my carrier for any issue with my messages not coming through. This may not be the most common caller problem, but it is certainly a known issue.

Implement RCS. Android phone makers and cellular carriers have started using Rich Communications Services, aka RCS, which brings the best of messaging apps to cross-operating system texting. It is faster and supports read receipts and typing indicators.

It sounds similar to what Apple originally envisioned for iMessage. “We approached the carriers to pursue adding features to the existing texting systems and removing the additional customer costs,” Mr. Forstall told me. “For various reasons, from the difficulty of extending the existing standards, to challenges with interoperability between texting systems and carriers, to the desire of carriers to protect a significant revenue stream, these explorations didn’t pan out.”

Apple hasn’t yet adopted RCS—which unfortunately isn’t end-to-end encrypted—but if it does, green-bubble messaging could look a lot more like blue-bubble messaging.

Bring iMessage to Android. This is the dream. Sure, it would make switching to Android easier, but here’s a business argument, Apple: Your loyal customers will be happier when messaging Android friends.

You see, many of us don’t need walls to keep us locked in. We just want to stop separating everyone into green and blue bubbles. The world is divided enough.

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Write to Joanna Stern at joanna.stern@wsj.com