For a start, there'd be commercial advantages to be had in offering a non-halal option.
Quite the opposite, which is why most producers do it this way, and most retailers and caterers choose halal meat as the cheaper option. Their meat can be eaten by Muslims and non-Muslims alike, which vastly simplifies many steps of the process.
And it's only fair.
Seriously? I think the number of things about a theistic state that are unfair and socially divisive and have measurable impacts on the lives of many people is significant, and 'someone prayed near my food' is nowhere near the top. When people focus on this one I'm afraid it does come across as wanting to make it harder for other people to practise their religion.
You care about an issue? You need to be prepared to put the work in. Campaign. Write to the producers and explain to them why they've got it wrong on what's commercially beneficial to them. Email a retailer and find it what they actually sell. Spend two minutes on google.
Living in a multicultural, tolerant society means that sometimes we rub up against things we don't like, or don't believe in, or feel weird. We can either engage in a bit of give and take - evaluate why it makes us feel icky, see if the issue really affects us and if so, change our own behaviours a little to help us all rub along together. Or we can solidly plough our own furrow and complain vociferously every time the system does not cater to our exact tastes.
I think religion is total bollocks, I think the state should be secular, but I don't have any great interest in stopping anyone practising their own religion as long as they don't seek to impose their beliefs on me.
My own view is that a prayer said near my food isn't imposing anything on me, because no one is asking me or my kids to join the prayer or even be present while it's said. It means the producers' costs are lower so my meat is cheaper, so it even benefits me. I have other issues about theism in society that trouble me greatly, and I put extra effort into those areas - things like education.
Your own views may differ, and that's fine. But it doesn't mean the system needs to be set up to cater to your specific ethics, any more than they do mine. There are products and producers out there that are fine for what you say you want (I even provided a helpful news article). They may cost a little more and you may have to go a little further. Beliefs and ethics come at a cost sometimes.